CONTINUOUS MICRODIALYSIS OF BLOOD PROTEINS DURING ...

CONTINUOUS MICRODIALYSIS OF BLOOD PROTEINS DURING

CARDIOPULMONARY BYPASS

by

ALEXANDER FOK

A Thesis submitted to the

Graduate School – New Brunswick

Rutgers, The State University of New Jersey

And

The Graduate School of Biomedical Sciences

University of Medicine and Dentistry of New Jersey

in partial fulfillment of the requirements

for the degree of

Master of Science

Graduate Program in Biomedical Engineering

written under the direction of

Professor Jeffrey D. Zahn

and approved by

_____________________________________

_____________________________________

_____________________________________

_____________________________________

New Brunswick, New Jersey

October 2009

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ABSTRACT OF THE THESIS

Continuous Microdialysis of Blood Proteins During Cardiopulmonary Bypass

By Alexander Fok

Thesis Director: Jeffrey Zahn, PhD

Cardiopulmonary bypass is a procedure that temporarily substitutes a patients’

heart and lung functions with an extracorporeal heart-lung machine. This allows surgeons

to operate on motionless heart and lungs, while still providing the body with proper blood

circulation. However, the heart-lung machine has been shown to activate the body’s

systemic inflammatory response, resulting in short- and long- term organ dysfunction,

and even death. The severity of this inflammatory response is strongly correlated to the

production levels of specific cytokines and complements found in the bloodstream.

Current detection methods require taking discrete blood samples during surgery and

waiting at least several hours, but typically one to two weeks when including laboratory

queue times in hospitals, for results. I propose a microdialysis device that continuously

samples the patient’s blood for biomarkers during surgery. The primary function of this

device is to prepare a purified solution, with complement concentrations that closely

matches that of the patient’s bloodstream, to be used in a continuous microimmunoassay

device.

The microdialysis device was fabricated using photolithography and

softlithography techniques to create microfluidic channels and bonded to commercially

available semi-permeable membranes with biocompatible epoxy. The device was

designed based on computational simulations and fabrication constraints for optimal

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performance. It was tested for its analyte-recovery capabilities for complements C3a,

C4a, and C5a, in human blood continually circulating through a mock heart-lung

machine.

Two slightly different designs were tested, one using a membrane pore-diameter

of 0.1 µm and the other using 0.4 µm. Both devices operated at a perfusion flowrate of

4.1 µL/min, which is considered to be relatively fast for microdialysis probes. For the 0.1

µm pore membrane device, the relative recoveries were 79%, 75%, and 70% for C3a,

C4a, and C5a, respectively. For the 0.4 µm pore membrane device, the relative recoveries

were 112%, 135%, and 101% for C3a, C4a, and C5a, respectively. These findings show

promising results for the proposed microdialysis device, but further investigation is

needed to improve statistical significance.

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ACKNOWLEDGEMENTS

This work would not have been possible without the guidance of my advisor, Dr.

Jeffrey Zahn. His combination of technical expertise and creative ideas has shown me

what it takes to approach new problems and how to solve them. I will continue to use

these lessons in whatever career comes my way and in my own life.

I would also like to thank our collaborator, Dr. Akif Undar, who has supported

this project in many ways. His generosity and willingness to share his laboratory space

and resources at Hershey Medical Center was vital for conducting experiments.

I thank my committee members, Dr. David Schreiber and Dr. Li Cai, who were

also my instructors at Rutgers University, for broadening my knowledge in the

biomedical engineering field. Their dedication to helping students learn has been

influential to me.

To my friends and colleagues at Rutgers University, I thank them for creating a

supportive and positive learning environment. Special acknowledgements go to the

members of my lab, whom I also consider as friends: Mercedes Morales, Kiana Aran,

Larry Sasso, and Pantelis Athanasiou, who have provided immense support with my

research and life in general.

To the faculty and administrative staff of Rutgers’ Biomedical Engineering

Department, I would like to express my appreciation for their help, advice, and friendly

demeanor that made for a pleasant experience at Rutgers University.

Finally, to the most important people in my life, I would like to thank my parents

and my brother for their seemingly infinite love and support.

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DEDICATION

To my family and friends for their love and support.

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TABLE OF CONTENTS

ABSTRACT OF THE THESIS ....................................................................................... ii

ACKNOWLEDGEMENTS ............................................................................................ iv

DEDICATION................................................................................................................... v

TABLE OF CONTENTS ................................................................................................ vi

LIST OF TABLES ........................................................................................................... ix

LIST OF ILLUSTRATIONS .......................................................................................... xi

Chapter 1 - Introduction .................................................................................................. 1

1.1 The Need for Microdialysis during CPB .............................................................. 1

Chapter 2 - Background ................................................................................................... 6

2.1 Cardiopulmonary Bypass Procedure .................................................................... 7

2.1.1 History of Development ................................................................................... 7

2.1.2 Main CPB Components ................................................................................... 9

2.1.2.1 Pumps......................................................................................................... 9

2.1.2.2 Oxygenators............................................................................................. 12

2.1.2.3 Heat Exchangers ..................................................................................... 13

2.1.3 Systemic Inflammatory Response ................................................................ 14

2.1.3.1 Inflammatory Cascade ........................................................................... 15

2.1.3.2 Complement System ............................................................................... 16

2.1.3.3 Red Blood Cell Damage.......................................................................... 18

2.1.3.4 Neutrophil and Vascular Endothelium................................................. 18

2.1.3.5 Organ Dysfunction.................................................................................. 20

2.1.3.6 Ischemia Reperfusion Injury ................................................................. 20

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2.2 Measuring Complement Components................................................................. 21

2.3 Microdialysis ......................................................................................................... 22

2.3.1 Development of microdialysis ....................................................................... 22

2.3.2 Basic Principles of Operation ....................................................................... 23

2.3.2.1 Perfusate .................................................................................................. 24

2.3.2.2 Membrane Material................................................................................ 25

2.3.3 Quantitative Microdialysis Models .............................................................. 27

2.3.4 Calibration Techniques ................................................................................. 28

2.3.4.1 Flowrate Method ..................................................................................... 29

2.3.4.2 No-net flux Method ................................................................................. 29

2.3.4.3 Retrodialysis ............................................................................................ 31

2.3.5 Microdialysis on a Chip................................................................................. 31

2.3.5.1 Methods for integrating membranes into devices................................ 33

Chapter 3 - On-chip Microdialysis System................................................................... 35

3.1 Theory .................................................................................................................... 35

3.1.1 Mass Transfer Prediction.............................................................................. 35

3.1.2 Fluid Pressure and Resistance ...................................................................... 38

3.2 Device Design and Fabrication ............................................................................ 40

3.2.1 General Design Considerations .................................................................... 40

3.2.1.1 First design: no bifurcation.................................................................... 43

3.2.1.2 Final Design: Bifurcating Tree .............................................................. 44

3.2.2 Photolithography and Soft Lithography...................................................... 46

3.2.3 Bonding to membrane ................................................................................... 49

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3.2.3.1 Thermal.................................................................................................... 49

3.2.3.2 Thin film deposition ................................................................................ 51

3.2.3.3 Epoxy Stamping ...................................................................................... 52

3.3 Numerical Studies - Electric Circuit Model ....................................................... 53

3.3.1 Observing Trends from Matlab Code.......................................................... 59

3.4 Microdialysis Experiments................................................................................... 67

3.4.1 Experimental Setup: Glucose and PBS........................................................ 68

3.4.2 Results and Discussion: Glucose and PBS ................................................... 70

3.4.3 Introduction: Blood with Mock CPB Circuit .............................................. 73

3.4.3.1 Experimental Setup: Blood with Mock CPB Circuit........................... 74

3.4.3.2 Results and Discussion: 0.1 µm membrane .......................................... 77

3.4.3.3 Results and Discussion: 0.4 µm membrane .......................................... 80

3.4.3.4 Time Course Data ................................................................................... 82

Chapter 4 - Conclusions and Future Work .................................................................. 86

Bibliography .................................................................................................................... 89

Appendix A: Preliminary Experiments ....................................................................... 95

Appendix B: Matlab Code........................................................................................... 100

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LIST OF TABLES

Table 1: Photolithography recipe for 30 micron thick Perfusion Channel ....................... 48

Table 2: Photolithography recipe for 130 micron thick Reservoir Channel ..................... 48

Table 3: Whatman Nucleopore Polycarbonate Track-etched Membranes ....................... 59

Table 4: Finalized Microdialysis Design for CPB integration.......................................... 67

Table 5: 100 nm membrane: p-values, pairwise t-test. Blue/bold values denote acceptance

of the null hypothesis. ........................................................................................... 80

Table 6: 100 nm membrane: correlation coefficient......................................................... 80




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LIST OF ILLUSTRATIONS

Figure 1.1: A cardiopulmonary bypass machine being used during surgery [3] ................ 2

Figure 2. 1: The Gibbon type cardiopulmonary bypass machine first used in March 1955

by Kirklin’s team at the Mayo Clinic [1]................................................................ 9

Figure 2.2: Blood pump designs. (A) Two-roller, roller pump. The tubing sits on the

inner surface of the raceway. (B) Impeller pump with vanes connected to a

rotating shaft. (C) Centrifugal pump. The inner concentric cone rotates rapidly,

propelling blood radially outwards. [22] .............................................................. 10

Figure 2.A: Diagram of a hollow fiber membrane oxygenator and heat exchanger unit.

Blood flows through the heat exchanger, over temperature-controlled coils and

then enters the oxygenator, which is made up of woven strands of hollow fibers.

Oxygen flows from one end of the fiber to the other, supplying oxygen and

exchanging carbon dioxide with blood. [22] ........................................................ 13

Figure 2.B: Contact activation cascade systems that cause SIRS [26] ............................. 15

Figure 2.C: The three pathways of the complement system: Classical pathway,

Alternative pathway, and Lectin pathway [26]..................................................... 16

Figure 2.6: A cannula-based commercial microdialysis probe. The cannula tip is placed in

extracellular fluid or on bare tissue, where analytes diffuse across the membrane

and into the analyte-free perfusate solution. [64] ................................................. 24

Figure 2.D: Scanning electron micrographs of a polycarbonate hollow fiber: (a) cross-

sectional view; (b) outer surface; (c) cross-section under higher magnification.

[71]........................................................................................................................ 26

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Figure 2.E: No-net flux method. Net difference between the dialysate and perfusate

concentrations plotted against varying perfusate inlet concentration. The x-

intercept represents where the perfusate concentration is equal to the tissue

concentration. [67] ................................................................................................ 30

Figure 2.F: Graph showing an increasing interest in the microfluidics and membranes

field over the last 12 years. [Source: Rutgers University Libraries Searchlight,

with keywords: “microfluidics” and “membranes”]............................................. 32

Figure 3. 1: A side-view diagram showing the layer reservoir channels and the layer of

perfusion channels on opposite sides of a porous membrane [13] ....................... 36

Figure 3.2: Exploded view of the three main components (right to left): PDMS layer for

the reservoir channel, a thin polymer membrane, and a PDMS layer for the

perfusion channel. ................................................................................................. 40

Figure 3.3: Demonstrating how improperly aligned channels can affect the diffusion area.

Solid lines represent one layer of parallel channels and the dotted lines represent

the other layer. Left: proper alignment results in full overlap. Center: even a small

lateral shift can result in no overlap. Right: a small rotational shift can also reduce

overlap areas. ........................................................................................................ 42

Figure 3.4G: CFD analysis of the non-bifurcating channel design. Fluid enters from the

short channel on the left and exits on the right. Most of the flow goes through the

center channels, while the outer channel have negligible flowrates. .................... 44

Figure 3.5: Bifurcating channel design: a CFD analysis showing a surface plot of the

velocity field. Red denotes high velocity and blue denotes low velocity. At each

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bifurcation stage, the flowrate splits up equally. This is only a partial model due to

computational constraints. .................................................................................... 45

Figure 3.6: Stacked view of the perfusion layer (blue) aligned on top of the reservoir

layer (red). The staggered design in the bifurcating tree section is intended to

minimize interaction between the two layers, except for the main section in the

center..................................................................................................................... 46

Figure 3.7H: Dark-field masks for photolithography. Left: Perfusion mask. Right:

Reservoir mask...................................................................................................... 47

Figure 3.8: Soft-lithography steps used to create microfluidic channels in PDMS.......... 47

Table 1: Photolithography recipe for 30 micron thick Perfusion Channel ....................... 48

Table 2: Photolithography recipe for 130 micron thick Reservoir Channel ..................... 48

Figure 3.10: Schematic for the epoxy stamping procedure. A) a small amount of epoxy is

placed on top of a clean glass slide; B) an object with a flat edge, such as another

glass slide, is used as a squeegee on the epoxy until a thin, uniform layer of epoxy

remains; C) the first PDMS layer is placed onto the thin layer of epoxy, with the

channel side facing down; D) and E) a membrane is placed on top of the epoxy-

side of the first PDMS layer; F) steps A-C are repeated for the second PDMS

layer and aligned with the first layer under a dissection microscope. .................. 53

Figure 3.11: A circuit diagram representing the microdialysis chip. The reservoir side is

given a voltage source to represent the pressure source given by the CPB pump.

The perfusate side is given a current source to represent the predetermined

flowrate put out by a syringe pump. Resistors represent hydrodynamic resistance,

which is a function of channel geometry and fluid viscosity................................ 55

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Table 3: Whatman Nucleopore Polycarbonate Track-etched Membranes ....................... 59

Figure 3.12: Results from Matlab model: Perfusion flowrate recovery vs CPB Pressure,

for various pore sizes. ........................................................................................... 61

Figure 3.13: Results from Matlab model: Perfusion flowrate recovery vs Perfusion

flowrate, for various pore sizes............................................................................. 62

Figure 3.14: Results from Matlab model: Perfusion flowrate recovery vs Reservoir inlet

tubing length, for various pore sizes. .................................................................... 62


for various reservoir channel heights. ................................................................... 63


flowrate, for various reservoir channel heights..................................................... 64


tubing length, for various reservoir channel heights............................................. 64


for various perfusion channel heights. .................................................................. 65


flowrate, for various perfusion channel heights.................................................... 66


tubing lengths, for various perfusion channel heights. ......................................... 66

Table 4: Finalized Microdialysis Design for CPB integration.......................................... 67

Figure 3.21: A revised circuit diagram for the bench-top glucose/PBS experiments, based

off of Fig 3.11, where the reservoir channel is driven by a syringe pump, instead

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of a CPB pump. Thus, the reservoir inlet tubing resistance can be ignored and the

reservoir inlet is now represented with a current source....................................... 69

Figure 3.22: Theoretical (hollow) and experimental (solid) Volume Recovery values for

perfusion (diamond) and reservoir (square) outlets, versus varying reservoir

flowrates................................................................................................................ 71

Figure 3.23: Glucose concentration recovery for perfusion and reservoir channels, for

varying reservoir flowrates. Data shows that both channels end up with near-

identical concentrations for a wide range of flowrates, causing the data points to

overlap one another............................................................................................... 73

Figure 3.24: The setup for the mock CPB circuit experiments. A relatively small quantity

of blood flow is routed to the reservoir channel of the microdialysis device, via a

Luer connection at the sampling manifold on the arterial side of the oxygenator.76

Figure 3.25: Analyte concentration for the 0.1 µm membrane device: (left) C3a, (center)

C4a, and (right) C5a. Data represents an average of 6 data points over a 1.5 hour

period. A two-sample paired t-Test was performed, where H0 = two means are

equal. The asterisk (*) represents a statistical significance level, α<0.05. ........... 78

Figure 3.26: Relative recovery for the 0.1 µm membrane device: (left) C3a, (center) C4a,

and (right) C5a. Data represents an average of 6 data points over a 1.5 hour

period. The asterisk (*) represents a statistical significance level, α<0.05........... 79




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Figure 3.27: Analyte concentration for the 0.4 µm membrane device: (left) C3a, (center)

C4a, and (right) C5a. Data represents an average of 6 data points over a 1.5 hour

period. A two-sample paired t-Test was performed, where H0 = two means are

equal. The asterisk (*) represents a statistical significance level, α<0.05. ........... 81

Figure 3.28: Relative recovery for the 0.4 µm membrane device: (left) C3a, (center) C4a,

and (right) C5a. Data represents an average of 6 data points over a 1.5 hour

period. The asterisk (*) represents a statistical significance level. ....................... 81




Figure 3. 29: Time course data with error bars representing 2 standard deviations for C3a.

............................................................................................................................... 84


............................................................................................................................... 84

Figure 3.3 1: Time course data with error bars representing 2 standard deviations for C5a.

............................................................................................................................... 85

Figure A. 1: Various orientations of the channels: (left) reservoir channel is directly over

perfusion channel; (middle) reservoir channel is perpendicular to perfusion

channel; and (right) the two channels are offset laterally by one-half the channel

width. Arrows denote direction of flow. ............................................................... 95

Figure A. 2: Glucose recovery at the perfusion outlet shown in Fig. A.1 (left), “parallel”

configuration. ........................................................................................................ 96

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Figure A. 3: Glucose recovery at the perfusion outlet shown in Fig. A.1 (middle), “cross”

configuration. ........................................................................................................ 98

Figure A. 4: Glucose recovery at the perfusion outlet shown in Fig. A.1 (right), “shifted

parallel” configuration. ......................................................................................... 99

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Chapter 1 - Introduction

1.1 The Need for Microdialysis during CPB

Cardiopulmonary bypass (CPB) is a procedure where a patients’ heart and lung

functions are temporarily taken over by, what is commonly referred to as, an

extracorporeal “heart-lung machine” (Fig. 1.1) to maintain the circulation and

oxygenation of blood in the body. This procedure is usually necessary when a surgeon

needs to operate on a motionless heart or lung, such as when repairing internal heart

defects or heart valves [1], but can also be done on a beating heart, such as for minimally

invasive off-pump coronary artery bypass surgery [2]. The CPB circuit consists of:

pumps to circulate blood through the machine, an oxygenator to exchange carbon dioxide

with oxygen in the blood, filters to remove emboli and gas bubbles, ports to introduce

drugs such as the anticoagulant heparin and anesthesia agents, tubing to transport blood

from one part of the circuit to another, and cannulas to remove and deliver blood, to and

from, a patient’s circulatory system [1].

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Figure 1.1: A cardiopulmonary bypass machine being used during surgery [3]

Although cardiac surgeries are usually life-saving procedures and the patient is

typically only on the CPB pump for several hours, a major disadvantage of using a heart-

lung machine is the damage it imposes on the circulating blood due to hemolysis [4, 5]

and a systemic inflammatory response [6, 7]. As blood circulates through various

components in the circuit, it can experience high shear stresses, and be exposed to

immunological-activating surfaces and endotoxins, all of which may induce a systemic

inflammatory response. As a result, short- or long-term multiple organ dysfunction, or

even death can occur [8-12].

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Researchers are currently working on correlating the expected degree of organ

dysfunction with the degree of a patient’s inflammatory response, which is done by

measuring blood for levels of specific biomarkers such as complements. Since

complement levels may fluctuate during and even after surgery, multiple discrete blood

samples are taken between pre- and post-surgery and sent to a lab for analysis, which can

typically take several hours to perform (though results may not be available for days or

weeks, depending on laboratory queue time). Given the ability to monitor complement

levels continuously and in near real-time, surgeons may be able to prevent or limit organ

dysfunction by administering therapeutic drugs at times and doses tailored to individual

patients.

This thesis is based on previous work and advances made by Zahn’s group in the

field of microfluidics and microfabrication. Hsieh et al. developed an on-chip, continuous

microdialysis and glucose sensing device for the treatment of diabetic patients [13, 14].

This device incorporated a microdialysis device with in-line sensing electrodes to

continuously track concentration changes with impressive glucose recovery and sensing

capabilities. Yang et al. developed a microfluidic device that continuously separate

splasma from whole blood [15] and another device that continuously monitors blood

plasma proteins via fluorescence intensity detection using biotinylated FITC solution and

streptavidin-coated microbeads [16], both devices utilizing the Zweifach-Fung effect [17,

18].

In this work, a microdialysis chip capable of continuously dialyzing blood

proteins, while excluding cells, is presented. The device uses photolithography and

softlithography techniques to fabricate microfluidic channels on a biocompatible

4

polymer, and an epoxy stamping technique to directly bond two layers of microchannels

on opposite sides of a porous membrane. The porous membrane allows for small analytes

in blood, such as proteins, to cross the membrane into an analyte-free, isotonic solution

while preventing cells and large cellular fragments from crossing and contaminating the

aforementioned isotonic solution.

In Chapter 2, some background information about the invention, design, and

detrimental effects of the heart-lung machine (CPB pump) are discussed. The design of

these components, such as the oxygenator and blood pumps, has a significant impact on

the degree of a patient’s inflammatory response. Current microdialysis techniques are

also introduced here.

In Chapter 3, the methodology for designing the proposed microdialysis chip is

explained as well as the fabrication techniques used. Initial bench-top experiments were

performed using a saline solution doped with glucose, using the sugar molecule as the

analyte of interest, and an analyte-free saline solution as the perfusate. Glucose recovery

ranged from 91% to 95%, over a broad range of flowrates, despite large pressure gradient

changes across the membrane. Further experimentation was performed on a mock CPB

circuit using a full heart-lung machine setup but with several units of human blood in a

blood bag instead of using an actual patient. The concentration levels for complements

C3a, C4a, and C5a were measured at constant flowrate settings, over a period of 90

minutes, for a device using 0.1 µm pore diameter membrane and another using 0.4 µm

pore diameter membrane. Analyte recovery performance varied depending on the pore

size of the membrane as well as the specific complement being measured.

5

Finally, conclusions and future works are discussed in Chapter 4. Though

inconsistencies were observed, the overall results show a promising path for designing an

improved microdialysis system. Based on the evidence from the experiments, further

investigation is necessary to explain several inconsistent observations such as why

complement levels in blood samples from the CPB circuit were sometimes lower than

that of the recovered dialysate; and why the complement levels in the solution recovered

from the reservoir channel’s outlet were significantly lower than that of the blood flowing

in the CPB circuit. The system should then be incorporated into a microimmunoassay

chip, which would continuously measure analyte concentration directly on the chip itself.

6

Chapter 2 - Background

In this chapter, CPB, its development, usage, and physiological complications are

introduced. Studies have shown that the body induces systemic inflammatory responses

during cardiac surgery, especially when cardiopulmonary bypass is used [11, 19-32].

Although much time and effort have gone into developing each component of the CPB

machine, almost every component is still responsible for cell damage and immune

activation to some degree. Clinical evidence has shown a strong correlation between

specific inflammatory response levels with postoperative complications, such as organ

dysfunction, which can potentially lead to death. At present, studies are done by taking

blood samples from the patient pre-, during, and post-operation. Typically, concentration

levels are then analyzed via enzyme-linked immunosorbent assay (ELISA) or immuno-

fluorocytometry. By being able to monitor a patient’s inflammatory response in near-real-

time and continuously during CPB, doctors may one day be able to offer effective

treatments during surgery, or at least understand the syndrome and its causes better.

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2.1 Cardiopulmonary Bypass Procedure

Today, over 400,000 open-heart operations are performed each year in the United

States [1]. Cardiopulmonary bypass is a procedure that replaces the function of the heart

and lungs during operations that require the patients’ own heart and lungs to be stopped.

A cardiopulmonary bypass pump (often referred to as heart-lung machine or mechanical

pump-oxygenator) is used to maintain the patient’s blood circulation, which keeps tissues

alive by providing nutrients and supplying oxygen to the blood while removing carbon

dioxide. This procedure is used on patients ranging from neonates to seniors and for

reasons ranging from heart-lung transplants to cardiac valve repair and/or replacement.

2.1.1 History of Development

During the 1930’s and 1940’s, prior to the invention of the heart-lung machine,

only simple extracardiac (outside of the heart) surgeries were possible. As doctors gained

experience and confidence from this, they began to expand into intracardiac surgeries,

where repairs are made inside the heart [1]. In order to support a patient’s life during this

more complex type of cardiac repair, surgeons had to somehow support the patient’s

blood circulation and blood-gas transfer. While several worldwide teams began to work

on mechanical pump-oxygenators, C. Walton Lillehei, at the University of Minnesota,

developed a controlled cross circulation procedure where another person’s oxygenated

blood (typically the patient’s parent) was cannulated from their femoral vessel and

pumped into the patient requiring cardiac repair [26]. Lillehei began clinical cases in

1954 and observed a 40% mortality rate (18 deaths out of 45 total cases) [33]. This

procedure also introduced potential risk to the donor. Nevertheless, the procedure was

8

seen as a success and many recommended abandoning further research into mechanical

CPB pumps.

John H. Gibbon, Jr. developed his CPB machine while working at Jefferson

Medical College in Philadelphia, PA, with partial financial support from Thomas J.

Watson, chairman of IBM. In 1952, Gibbon’s first attempt at using his mechanical pump

with a screen oxygenator was unsuccessful due to a fatal misdiagnosis of the one year old

patient’s condition [1]. Gibbon’s only success with his machine came in May 1953 for an

18 year old woman suffering from atrial septal defect (ASD). Gibbons made several more

unsuccessful cardiac surgical attempts, but the patients died and no further attempts were

made [1].

In 1952, John W. Kirklin gathered a team of experts in pathology, physiology,

cardiology, anesthesiology, and mechanical engineering at the Mayo Clinic to develop a

mechanical pump-oxygenator. Using the Gibbon-IBM machine’s blueprint as a starting

point, Kirklin modified and refined the design for 2½ years before its first use in 1955

(Fig. 2.1). In that year, a clinical series of open heart surgeries where Gibbon’s CPB

pump was used on 8 patients (aged between 4 months to 11 years old), where 4 died

postoperatively. Patients were under cardiopulmonary bypass for 20 to 73 minutes, with

blood flowrates of 100 ml/kg [34]. This pioneering effort led by the Mayo Clinic team,

brought forth a new era in intracardiac surgery.

9

Figure 2. 1: The Gibbon type cardiopulmonary bypass machine first used in March 1955 by

Kirklin’s team at the Mayo Clinic [1]

2.1.2 Main CPB Components

A modern-day CPB machine consists of two main components: the pump and the

oxygenator. Secondary components are tubing, which connects components from one

part of the circuit to another, and cannulae, which are tubes that connect to the patients’

veins and arteries. Each component has continually gone through design changes, with

the motive of minimizing physiological effects such as systemic inflammatory response,

hemolysis, and microembolisms.

2.1.2.1 Pumps

Performance characteristics that an ideal CPB pump should have are: 1) the

ability to pump blood at 7 l/min against a pressure of 500 mm Hg for an adult, 2) should

not cause damage to cellular or acellular blood components, 3) should not have dead

10

spaces where blood can stagnate or experience turbulent flow, 4) reproducible pump

flowrates, and 5) ability to be operated manually in case of power failure [26]. Roller

pumps and centrifugal pumps, as seen in Fig. 2.2, are the two most common types of

extracorporeal pumps currently used for blood perfusion.

For the last five decades, the roller pump has been the most commonly used type

for CPB, though recent improvements in centrifugal pumps have helped them gain

popularity. In a roller pump, a length of tubing is located alongside a curved raceway,

which is placed at the travel perimeter of rollers mounted on the ends of rotating arms.

The arms are oriented such that at least one roller pinches the tubing at all times. As the

roller begins to pinch the tubing at the beginning of the raceway, the volume of blood in

the tubing ahead of the pinched section is pushed forward. This action allows for

continuous blood flow, where flowrate is determined by the inside diameter of the tubing

and the speed of the rollers moving along the raceway. Although pumps with varying

amounts of rollers exist, a two-roller pump provides a relatively nonpulsatile flow

compared to a single-roller pump and causes less hemolysis than a multiple-roller pump.

Figure 2.2: Blood pump designs. (A) Two-roller, roller pump. The tubing sits on the inner surface of

the raceway. (B) Impeller pump with vanes connected to a rotating shaft. (C) Centrifugal pump. The

inner concentric cone rotates rapidly, propelling blood radially outwards. [22]

11

When using roller pumps, several complications can arise during an operation. If

a blockage occurs somewhere in the outflow end, pressure in the line can increase

progressively until a tubing or connector fails. If a blockage occurs somewhere in the

inflow end, a high negative pressure in the line can induce blood cavitation (the

production of microscopic air bubbles) or suction of room air through loose valves or

connections. Normal wear in the tubing, caused by the rollers, can create pinhole leaks,

where microscopic air bubbles can enter the line and head towards the patient [35]. In a

study by Stoney et al., line embolism from roller pumps were responsible for 92 deaths

and 61 permanent injuries between 1972 and 1977 [36].

Centrifugal pumps have already replaced roller pumps at many institutions. Its

basic design components consist of an impeller with a series of vanes or a stack of

smooth plastic cones inside a plastic housing. The impeller is either driven directly by a

shaft or indirectly by a magnetic coupling. Typically, fluid enters at the center of rotation.

Then, as the impeller rotates, the fluid is propelled radially outwards due to centrifugal

force, where it exits the pump. Unlike roller pumps, which rely on some amount of

occlusion (closure via pinching) in the tubing, centrifugal pumps are nonocclusive.

Because of this, the degree to which centrifugal pumps can experience extreme positive

or negative pressures are low, when compared to roller pumps. Therefore, the chances of

cavitation and microembolism issues are reduced [35]. Another major advantage is the

reduced risk of introducing macroscopic and microscopic air bubbles, possibly due to a

combination of shear force and positive pressure generation within the pump head [26].

Centrifugal pumps also suffer from several disadvantages. Due to the centrifugal

pump’s nonocclusive design, retrograde flow is possible when the pump stops or slows.

12

Also inherent to this design, even when the rotational speed is fixed, the flowrate can

change automatically when the systemic vascular resistance changes; therefore the

arterial outflow must be monitored with a flow probe.

Although both types of pumps mentioned have advantages and disadvantages, the

medical community has not been able to reach a unanimous opinion on which is

ultimately safer for patients. Some studies have shown less hemolysis with centrifugal

pumps versus roller pumps [37, 38], while others have shown contradictory results [39,

40] or no difference at all [41, 42].

2.1.2.2 Oxygenators

Oxygenators serve several purposes during CPB, besides oxygenating blood. It

acts as an entry point for anesthesia, and as a gas exchanger for oxygen, carbon dioxide,

and other gases. They also serve as a heat exchanger and blood filter. Because of the

natural lung’s complex and highly efficient structures of pulmonary alveoli and

capillaries, the artificial lung was one of the primary challenges for CPB designers.

Although several types of membrane oxygenators exist, the cross-current hollow

fiber membrane (Fig. 2.3) is most commonly used. The hollow polypropylene fibers have

pores of 1 µm in diameter that prevents both gas and blood from crossing the membrane.

Fresh air flows through the inside of bundles of hollow membrane fibers, while blood

flows perpendicularly outside of the fiber. The cross-flow design takes advantage of

secondary-flow that is induced by the fibers “tripping” fluid flowing past it, which

reduces the diffusion boundary layer and improves gas exchange.

13

Figure 2.A: Diagram of a hollow fiber membrane oxygenator and heat exchanger unit. Blood flows

through the heat exchanger, over temperature-controlled coils and then enters the oxygenator, which

is made up of woven strands of hollow fibers. Oxygen flows from one end of the fiber to the other,

supplying oxygen and exchanging carbon dioxide with blood. [22]

2.1.2.3 Heat Exchangers

Heat exchangers are coupled with the oxygenator and can either cool down or

warm up blood circulating through it. Typically, blood flows through spiraling coils made

of stainless steel or aluminum, which are submerged into circulating non-sterile water.

The inner walls of the coils are coated with polymers to limit blood-surface interactions.

The circulating water is chilled to nearly 0oC in an ice bath and heated by an electric

resistance coil to an absolute maximum of 42oC, at which point blood proteins begin to

denature [26]. Blood temperature plays a crucial role during CPB, as it can lead to serious

short- and long-term health issues for the patient.

14

Inducing hypothermia at the onset of CPB reduces the patient’s metabolism,

blood oxygen requirements, complement activation, and overall systemic inflammation

[1, 10, 43]. The blood is cooled as quickly as possible and is only limited by thermal and

fluid dynamics. Conversely, re-warming of the blood is performed at the end of the

procedure and its heating rate is carefully controlled to prevent blood damage, which can

ultimately lead to cerebral injury. Furthermore, overheating blood too quickly can

produce bubble formation due to the decrease in gas solubility, producing gaseous

microemboli.

2.1.3 Systemic Inflammatory Response

SIRS, an acronym for “systemic inflammatory response syndrome,” is a term

used to associate cardiopulmonary bypass with a wide range of ailments due to a “whole

body” inflammatory response such as pulmonary, renal, gut, central nervous system, and

myocardial dysfunctions; vasoconstriction; vasodilatation; hemolysis; leukocytosis; and

an increased risk to infections [11, 27, 28, 32, 35, 44]. Neither the severity of the

response nor the specific ailment(s) to occur, are predictable. However, the duration of

CPB, age, and complexity of the procedure are commonly regarded as risk factors [23,

27, 45, 46].

The origin of SIRS response can be attributed to the damage of cellular and

noncellular (humoral) components of blood, primarily caused by altered arterial blood

flow patterns and blood-surface contact within CPB components [26]. This can then

result in microemboli formation, hemostasis disruption, and most importantly, a chain-

reaction of cytokine-mediated and neutrophil-mediated inflammatory injury.

15

2.1.3.1 Inflammatory Cascade

The inflammatory cascade is primarily caused by the activation of factor XII, a

plasma protein, to factor XIIa, which triggers several inflammatory systems (Fig. 2.4). To

start, surface contact causes factor XII to undergo a conformational change and become

attached to high-molecular-weight kininogen [26]. This complex then adheres to the

foreign surface, undergoes limited proteolysis, then releases kallikrein, bradykinin, and

factor XIIa. A positive feedback system involving factor XIIa and kallikrein, which

activates neutrophils, can further activate the inflammatory cascade via production of

oxygen free radicals and proteolytic enzymes [26].

Figure 2.B: Contact activation cascade systems that cause SIRS [26]

16

2.1.3.2 Complement System

The complement system plays several key roles in the inflammatory process, such

as mediating inflammation, opsonization of antigenic particles, and damaging pathogen

membranes [26]. The product from a complement component interaction becomes the

enzyme for the next step, as shown in Fig. 2.5. The complement system cascade can be

triggered by just a small initial stimulus and result in massive amplification of the initial

activating event. Fortunately, this system is tightly controlled by regulatory molecules,

which makes up half the proteins in the complement system.

Figure 2.C: The three pathways of the complement system: Classical pathway, Alternative pathway,

and Lectin pathway [26]

17

There are two activation pathways in the complement system: the classical

pathway and alternative pathway. The classic pathway, which is the least important in

this discussion, is initiated when antibodies bind to target antigens on a surface. Its

cascade leads to the production of the classical pathway C3 convertase, C4b2b. This

convertase then cleaves C3, the central component of the system, into C3a and C3b

fragments. The alternative pathway has a feedback loop that begins at the C3b component

and leads to the generation of the alternative pathway C3 convertase, C3bBbP. This

convertase also cleaves C3 into its C3a and C3b fragments, where the C3b product can

then be re-initiated to the beginning of the alternative pathway. Although the spontaneous

activation of C3 occurs on a continuous basis, albeit at a low level, the triggering of the

full cascade can be prevented by cellular expression of regulatory proteins that inactivates

C3bBbP [26].

A third and final pathway in the complement system is the lectin pathway. This

pathway uses C3b, from either the classical or alternative pathway, to activate C5 to

produce C5a and C5b. C5a is a soluble molecule, while C5b binds to cell surfaces. As a

result, C6, C7, and C8 binds to the cell surface and C9 polymerizes to form a pore

through the cell membrane; thus resulting in a membrane attack complex (MAC) [26].

During CPB, activation of the complement system can be observed by monitoring

the consumption of components [47] and the presence of C3a and C5a in the circulation

[26]. Several factors have been shown to activate the cascade during CPB including:

surface biocompatibility, release of endotoxin into the system, and the breakdown of C3

caused by blood interaction with oxygen bubbles.

18

2.1.3.3 Red Blood Cell Damage

Red blood cells (RBCs) primarily damaged by shear stress have reduced

deformability due to mechanical damage [48]. Red blood cell deformability affects the

rheological properties of blood and is particularly important to maintain tissue

metabolism and oxygenation. Membrane damage also disrupts the normal function of

ionic pumps and causes an abnormal accumulation of cations within the cell [49]. The

membrane attack complex (MAC), generated during complement activation [11], attacks

the plasma membrane by forming pores, which allow free diffusion of molecules to pass

in and out of the cell. When enough pores are formed, hemolysis can occur. Death or

even damage to RBCs may be one reason for post-operative anemia frequently observed

in patients[50], as RBC damage shortens cell lifespan.

Besides anemia, RBC injury has a destructive effect at cellular, tissue, and organ

levels. An increase in plasma hemoglobin levels increases the plasma oncotic pressure

and viscosity, which is detrimental to tissue function. The auto-oxidation of hemoglobin

releases cytotoxic oxygen free radicals. Potassium released from RBCs and into

extracellular fluid may impair cardiac conduction and cause arrhythmias. Fragments of

RBC lipid membranes can also block microcirculations (arterioles, capillaries, and

venules) and cause organ dysfunction.

2.1.3.4 Neutrophil and Vascular Endothelium

Neutrophils make up most of the leukocytes in the body and are essential against

fighting infections and foreign materials. On the other hand, activated vascular

endothelium triggers neutrophil activation when the two come into contact, resulting in

19

much of the SIRS maladies. CPB circulation triggers a humoral cascade that leads to the

activation of the vascular endothelium. Neutrophil activation occurs via IL-8, C5a, or

platelet activation factor (PAF) to express adhesion molecules on its surface, causing the

activated neutrophils to adhere to activated endothelium. At this stage, cytotoxic

proteases and oxygen-derived free radicals are released by the neutrophils, causing some

of the post-CPB end-organ damage [26].

Under normal physiological circumstances, the vascular endothelium is relatively

inert and allows blood to circulate freely. Inflammatory signals (such as complement

activation products, oxygen-derived free radicals, and cytokines) cause the endothelial

cells to change their gene expression, prompting the release of cytokines and protein

expressions, which leads to inflammatory reactions and thrombosis [19, 51]. Typically,

endothelial activation occurs at a local site, where neutrophil recruitment and coagulation

can occur to contain the local infection. However, cytokines released during CPB causes

this reaction to occur on a systemic level. As a result, large areas of endothelium are

activated, followed by large scale neutrophil activation, adhesion, and release of

cytotoxic proteases and oxygen-derived free radicals. The body’s feedback mechanism

that is normally able to cope with attenuating the response at a local level is not able to

cope proportionately at a systemic level. End-organ damage, microemboli, and clotting

factor depletion are contributing factors to coagulopathy (clotting disorder) complications

after open-heart surgery [24, 25, 52, 53]. Neutrophil-endothelium adhesion can cause

capillaries to become blocked, causing local ischemia [20]. Finally, cytotoxic products

released by activated neutrophils can damage cells directly.

20

2.1.3.5 Organ Dysfunction

Organs that are affected by CPB may include: the lung and pulmonary circulation,

kidneys, brain, and gut. At the end of CPB, the entire cardiac output is sent to the

pulmonary circulation, which will be exposed to a large number of activated cells passing

through. Studies have shown that activated neutrophils are more likely to become lodged

in the pulmonary circulation [54, 55] and release free radicals that cause lung injury.

Studies have shown that intravenous injection of oxygen radical scavengers, such as

superoxide dismutase or catalase, can attenuate pulmonary damage [56]. Renal function

is reduced by the effects of (CPB-induced) hypothermia, which increases vascular

resistance and vasoconstriction. To remedy this during CPB, hemodilution is used to

improve plasma flow and help prevent renal injury [31]. Blood cell aggregates

(microemboli) can cause brain swelling and lead to postoperative cerebral dysfunction

[57].

2.1.3.6 Ischemia Reperfusion Injury

During an on-pump open heart surgery, where the heart is intentionally stopped

and isolated from blood circulation via an aortic cross-clamp, the heart tissue is damaged

due to the lack of oxygen and nutrients, and inability to remove metabolic waste [26].

However, further injury is incurred when blood flow is reintroduced, towards the end of

surgery; this is known as ischemia reperfusion injury. Several mechanisms of reperfusion

injury exist, including: oxidative stress, where the oxygen in the returned blood exposes

cells to damaging oxygen free radicals; neutrophil activation, partially caused by blood

contact with extracorporeal surfaces; and activation of the complement cascade, primarily

21

through the alternative pathway, which produces complement fragments (such as C3a and

C5a) that further activates neutrophils [58]. Examples of reperfusion injury include

myocardial necrosis, endothelial dysfunction, and apoptosis [26]. By monitoring the

levels of specific biomarkers such as complement fragments in circulating blood, it

would be possible to finely tuned doses of complement pathway inhibitors to counteract

the inflammatory response in near-real-time.

2.2 Measuring Complement Components

Immunoassay techniques used in hospitals today (such as radioimmunoassay,

enzyme-linked immunosorbent assay, or cytometric bead assay kit) involve machines that

are typically cumbersome and expensive to operate. Multiple sample-preparation steps

are required from the end-user, especially if the sample contains whole blood. Blood

samples must be collected in tubes and kept on ice until it is ready to be centrifuged at

4oC, at which point, the separated plasma is extracted and frozen at -70

oC [59, 60]. The

centrifuging process removes red blood cells, leukocytes, platelets, and other debris from

plasma since there is evidence that shows blood stored at 4oC contributes to complement

activation via the classical or alternate pathway [61]. Another contributing factor via the

alternate pathway has been reported to be a result of blood contacting plastic surfaces

during storage [62]. As one can see, careful steps must be taken to ensure validity of the

samples such that there is no change in complement concentration from the time at which

they were collected.

22

2.3 Microdialysis

Microdialysis sampling is a technique used to collect analytes from extracellular

fluid (ECF) for analysis. The primary component of all microdialysis devices is its semi-

porous membrane that is placed in between ECF and perfusion fluid. Substances travel

from areas of higher concentration to lower concentration. Small analytes from the ECF

(such as proteins, peptides, and other chemicals) diffuse through the membrane pores and

into the perfusate while large particles (such as cells, platelets, large proteins, etc.) are

excluded. In other words, the device provides “clean” samples to make chemical analysis

easier or even possible.

2.3.1 Development of microdialysis

Microdialysis sampling began as a means to measure the chemical composition

from rodent brain in real-time. By placing a microdialysis probe at specific target sites

instead of using a needle to draw blood samples from the bloodstream, it provides both

temporal and spatial references to the data. Today, it is used essentially on every organ

for applications ranging from endocrinology, immunology, metabolism, and

pharmacokinetics, though a vast majority of biomedical literature has focused in

neuroscience [63]. However, more and more life scientists are realizing the potential uses

for microdialysis sampling beyond neuroscience.

23

2.3.2 Basic Principles of Operation

Currently, microdialysis sampling devices most commonly exist in the form of a

microdialysis probe located at the tip of two concentric cannulae (the “inner” cannula and

“outer” cannula) (Fig. 2.6). Depending on the organ’s fragility, the cannulae can be made

out of rigid or flexible materials. The perfusion fluid (“perfusate”) flows down the

interior of the inner cannula, where it exits the tip of the inner cannula, and then flows

upwards (away from the tip) in between the outer and inner cannulae. At the probe end, a

section of the outer cannula is made of a semipermeable membrane and is the region that

comes into direct contact with the tissue site or fluid-filled space. Analytes from the

probe’s exterior diffuse across the membrane and into the perfusion fluid (referred to as

the “dialysate”), where it then exits the microdialysis device to be collected or analyzed

further downstream.

24

Figure 2.6: A cannula-based commercial microdialysis probe. The cannula tip is placed in

extracellular fluid or on bare tissue, where analytes diffuse across the membrane and into the

analyte-free perfusate solution. [64]

2.3.2.1 Perfusate

The particular perfusate solution is chosen carefully to match the ionic and

osmotic strength of the ECF, which helps maintains fluid and ion balance across the

membrane. An improperly balanced osmotic pressure across the membrane can cause

perfusion fluid to be gained or lost, thereby affecting the analyte concentration to be

measured as well as the normal physiological environment. An improperly balanced

ionic gradient across the membrane can also damage sensitive organs such as the brain.

For these reasons, a form of Ringer’s solution is used as the perfusate and typically

contains 150 mM NaCl, 4 mM KCl, and 2.4 mM CaCl2. The solution can also be

25

supplemented with glucose and ionic salts [64]. If properly balanced, the primary mode

of transport is diffusion, driven by the analytes’ concentration gradients.

2.3.2.2 Membrane Material

The same semipermeable porous hollow fiber membranes used in kidney dialysis

is also used in microdialysis probes (Fig. 2.7). Until recently, membranes were only able

to recover low-molecular mass mediators, metabolites, and xenobiotics. With the current

availability of high molecular weight cutoff (MWCO) membranes, larger molecules such

as plasma proteins, complements, and growth factors can now be recovered as well [65].

Commonly used materials include polycarbonate/polyether blends (PC), polyethersulfone

(PES), polyacrylonitrile (PAN), and cuprophan (CUP), and can have MWCO ranging

from 5 kDa to 100 kDa. Due to its manufacturing process, porous hollow fiber

membranes are made up of a range of pore sizes and its pore size distribution can be wide

or narrow. The manufacturers typically define MWCO as the absolute maximum

molecular weight by which anything greater is rejected but only a small fraction of

molecules at or near that molecular weight will pass through (typically significantly less

than 1%). As another example, a 10 kDa protein crossing a commercial 100 kDa MWCO

membrane at a perfusion flowrate of 1 µl/min typically has a relative recovery below 5%

[66], where relative recovery is simplified to be defined as the ratio of concentration

“recovered” at the perfusion outlet to the concentration at the target site. A more in-depth

explanation of this term is given in the next section.

A common problem associated with large MWCO membranes during

microdialysis is ultrafiltration. Ultrafiltration occurs when the perfusate side of the

26

membrane is over-pressured, driving a convective flow of perfusion fluid through the

pores and out of the probe. This is seen more commonly in large MWCO because of the

inherently lower hydraulic resistance in the pores. If observed, the perfusion flow rate

should be decreased since ultrafiltration dilutes analyte concentration in the tissue.

A membrane’s MWCO cannot be relied upon as a good predictor for recovery

performance during microdialysis [67]. The interaction between membrane material

(“chemistry”) and a particular analyte can also affect performance. For example,

hydrophobic analytes are difficult to recover [68, 69], with little exception [65], and

negatively charged analytes are typically rejected by negatively charged membrane

materials such as polyacrylonitrile [70].

Figure 2.D: Scanning electron micrographs of a polycarbonate hollow fiber: (a) cross-sectional view;

(b) outer surface; (c) cross-section under higher magnification. [71]

27

2.3.3 Quantitative Microdialysis Models

The microdialysis extraction fraction, Ed, or relative recovery, of a probe-styled

microdialysis setup is defined as:

Recovery = Ed in

inout

CC

CC

−

−=

∞

Equation 2.1

where Cin, Cout, and C∞ are the concentrations for the analyte of interest in the inflow

perfusate, outflow dialysate, and the tissue/fluid surrounding the probe, respectively. The

perfusate flowing into the probe is normally devoid of the analyte of interest (Cin equals

zero) and thus the equation can be simplified to:

Recovery = Ed ∞

=C

Cout Equation 2.2

In other words, the recovery term is a measure of how efficient the microdialysis probe

(perfusate) is able to represent the analyte concentration in the tissue or solution.

Bungay et al. developed a steady-state mathematical model [72, 73] to calculate

the expected microdialysis extraction fraction, Ed, from a constant concentration

stationary ECF, given by:

Ed

++−−=

−

−=

∞ )(

1exp1

emddin

inout

RRRQCC

CC Equation 2.3

where Qd is the perfusion flow rate and Rd, Rm, and Re are the dialysate, membrane, and

external medium resistances, respectively. Analytes sequentially diffuse across a region

of the external medium, then the membrane, and finally through to the dialysate in order

to exit the microdialysis probe. Since these resistances are in series and mass transfer

flow is conserved (i.e. equivalent) across the three regions, the resistances are additive.

Eq. 2.3 assumes that the transmembrane pressure is sufficiently small and that there is no

28

convective fluid flow through the membrane; that is, mass transport is primarily due to

diffusion across a concentration gradient [13].

Jacobson et al. developed an empirical model [74] that related microdialysis

extraction with the perfusion flowrate, active area of the membrane, and the mass transfer

coefficient. The resulting equation is:

)/exp(1 0 d

out QAKC

C−−=

∞

Equation 2.4

where K0 is the analyte-specific mass transfer coefficient for the membrane, A is the

active area of the microdialysis membrane, and the remaining terms are described

previously. Extrapolating this equation to the case of zero flowrate reveals that Cout is

expected to equal C∞, i.e., resulting in full recovery of the analyte. The product (-K0A) is

equivalent to resistance terms, 1/( Rd + Rm + Re), from Eq. 2.3, and the entire expression

is equivalent to Bungay’s expression for Ed in Eq. 2.3. Jacobson’s group realized that

different amino acids, even with similar molecular weights, exhibited different in vivo

mass transport coefficients. Therefore, for most cases, K0 values must be determined

experimentally for each analyte-membrane combination.

2.3.4 Calibration Techniques

Obtaining the true interstitial concentration of an analyte (i.e. 100% extraction

efficiency) via microdialysis is difficult with today’s microdialysis probes, as it requires

the perfusion flowrate to be extremely low. Typical sampling flowrates range between

0.5 and 2.0 µl/min [63] and even then, the dialysate will typically have an Ed of less than

30% at 0.5 µl/min and less than 20% at 1.0 µl/min for in vitro recovery of cytokines [75].

29

Operating at even lower flowrates increases the sample collection time significantly,

since there is always some minimum volume of sample required for analysis. Calibration

techniques allow for a more practical means of estimating what the true ECF

concentration is. Several approaches exist to approximate the true concentration, each

with their own limitations.

2.3.4.1 Flowrate Method

Jacobson et al. developed a calibration technique [74] known as the flowrate

method, or the mass transfer method, where the perfusion flowrate is decreased gradually

while changes in the dialysate concentrations are measured. At low flowrates, the change

in dialysate concentration plateaus. By applying appropriate nonlinear regression analysis

on this data, the concentration can be extrapolated for the zero flowrate condition, which

can be approximated to be the true tissue concentration value. However, this method is

not very accurate. Accuracy improves as lower and lower flowrates are used but this

incurs the problem of long collection periods as described earlier.

2.3.4.2 No-net flux Method

Unlike the previous method which uses analyte-free perfusate, another method for

calibrating the microdialysis probe involves perfusing known concentrations of the

analyte of interest into the probe at a specific flowrate and then measuring the dialysate

concentration that comes out (i.e. measuring before and after dialysis). This is known as

the no-net flux method, or equilibrium dialysis, and was first conceived by Lonnroth et al

30

in 1987 [76]. The left hand side of Eq. 2.3 is assumed to be an unknown value P since

neither the perfusion flowrate nor the resistances change. Thus it can be rearranged as

( )∞−−=− CCPCC ininout Equation 2.5

where P is the proportion of analyte transport to and from the probe. The net difference

between the dialysate concentration and perfusate concentration (Cout - Cin) is plotted as a

function of varying perfusate concentrations (Fig. 2.8). Then, a simple linear regression

analysis is performed. Whether the analyte ultimately diffuses into or out of the probe is

assumed to be solely due to the concentration gradient between what is added to the

perfusate and the tissue concentration itself. Theoretically, when the net difference (Cout -

Cin) is zero, it implies that the perfusate concentration is equal to the tissue concentration,

which is represented by x-intercept of the plot. This data from this technique is relatively

simple to analyze and does not necessarily require the use of slow perfusion flowrates

[73, 77].

Figure 2.E: No-net flux method. Net difference between the dialysate and perfusate concentrations

plotted against varying perfusate inlet concentration. The x-intercept represents where the perfusate

concentration is equal to the tissue concentration. [67]

31

2.3.4.3 Retrodialysis

The retrodialysis technique determines Ed by measuring the loss of an analyte

from the perfusate [78, 79]. The perfusate is doped with an analyte of known

concentration of at least ten times that of the tissue concentration surrounding the probe

[67]. For this method, it is necessary to dope the perfusate with an analyte that has very

similar diffusion characteristics as the analyte of interest. Usually, a radiolabled version

of the analyte of interest is used. High concentrations in the perfusate are required to

ensure that the radio-labeled analyte crossing the membrane (from perfusate-side to

tissue-side) is not limited by the concentration of unlabeled analyte (on the tissue-side),

regardless of the concentration on the tissue side of the membrane [77]. By this

assumption, C∞ is negligible compared to the known Cin and the extraction fraction can

be determined by

in

outin

dC

CCE

−= Equation 2.6

However, extremely high concentrations of radiolabled analyte in the perfusate tend to

make the membrane the diffusion-limiting site, and thus, should be avoided [80, 81].

2.3.5 Microdialysis on a Chip

Micrometer-scale total analysis systems (µTAS) are becoming more than just a

novel research concept and beginning to be considered an important tool to improve

global health. Also known as ‘lab-on-a-chip’ devices because of their likeness in size and

similar fabrication processes with computer microprocessors, they are used in diverse

applications such as biochemical assays, polymerase chain reactions, and blood sample

32

separation. Some advantages that microdevices offer include smaller volumes of reagents

and potentially hazardous wastes, reduced cost, portability, and speed of analysis. The

broad field of microfluidics has seen incredible advances in the last 20 years [82]

although the very first µTAS, a micro gas chromatograph, was developed at Stanford

University in the 1970s [83]. In particular, microfluidic devices using membranes for

mass transport control have been garnering increasing amounts of interest over the past

10 years, as illustrated in Fig. 2.9. Some µTAS applications involving membranes

include separation, purification, sample pre-treatment, and dialysis [84].

0

25

50

75

100

125

150

175

200

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

# articles with "microfluidics"

and "membranes" as keywords

Figure 2.F: Graph showing an increasing interest in the microfluidics and membranes field over the

last 12 years. [Source: Rutgers University Libraries Searchlight, with keywords: “microfluidics” and

“membranes”]

33

2.3.5.1 Methods for integrating membranes into devices

There are several basic fabrication techniques to incorporate membranes into

µTAS devices: membrane preparation during chip fabrication process, in situ preparation

of membranes, and directly incorporating (commercial) membranes. Each method offers

a series of advantages and disadvantages; ultimately, the decision depends on one’s

priorities for cost, ease of fabrication, MWCO control, and chemical compatibility.

One approach is to fabricate the membrane during the fabrication process of the

chip. That is, the pores are created directly on the microfluidic chip itself. Many

semiconductor microfabrication techniques are available to create pores in silicon wafers

such as electrochemical etching [85], back etching [86], and ion beam track etching [87].

Some major advantages with using clean room technology include: using well established

and understood semiconductor processes, excellent control of feature size (to the order of

tens of nanometers), ability to make tailor-made structures, and avoiding sealing issues

altogether. In fact, in most cases, there is no sealing process because the membrane is

created as part of the chip substrate itself [84]. However, just like most other uses of

semiconductor technologies, the production process is complex and expensive.

Another approach for integrating membranes is to fabricate them in situ on a pre-

made microfluidic chip. Several variations for this method exist but usually involve

selective polymerization. Polymerization of acrylate monomers occurs via UV light

exposure, where the position and thickness of the membrane can be controlled simply by

controlling where UV light hits [88]. Non-polymerized monomers are washed out

afterwards. MWCO properties can vary depending on the ratio of monomer and cross-

linking agent used, but ultimately requires trial and error experiments and educated

34

guesses for tailored specifications. The range of applicable materials is also very limited.

Membranes can also form via interfacial polymerization at the interface between two

solutions, as demonstrated by Kitamori et al. [89]. In this case, a thin polyamide

membrane was created at the interface of an organic and an aqueous solution, both

containing a certain monomer that reacts via a poly-condensation reaction to form. Again,

there is only a limited range of membrane materials.

Lastly, in-house or commercial membranes can be directly incorporated into

microfluidic devices by clamping or gluing the membrane between two microfluidic

chips; it is also the most straight-forward of the options. Commercial membranes are sold

as flat sheets and come in varying materials, sizes, and MWCOs and may undergo

surface modification to functionalize the membrane with trypsin [90] or bovine serum

albumin [91], for example. The clamping method offers flexible configurations because it

is possible to swap in/out different types of membranes depending on the application.

However, creating a good seal can be difficult. When clamping hard substrates such as

silicon and glass, the two surfaces that contact the membrane must have a high degree of

flatness and even pressure must be applied to prevent leaking. Also, capillary forces can

cause glue to get sucked into and block microfluidic channels and membrane pores.

In this thesis, a microdialysis chip intended for continuous dialysis of blood

proteins during cardiopulmonary bypass procedures is presented. The device sandwiches

a commercial membrane between two microfluidic chips and bonded with epoxy for cost

savings and ease of manufacturability. The microdialysis chip is designed with high

throughput, extraction efficiency, and robustness in mind.

35

Chapter 3 - On-chip Microdialysis System

In this chapter, a microdialysis chip is developed for continuous blood protein

extraction for, but not limited to, CPB operations. The fabrication steps are based on

semiconductor technology and soft lithography, both of which will be discussed in detail.

3.1 Theory

Fluid dynamics and mass transport theories are used to predict and explain the

performance of the microdialysis device. Optimization of overall device performance

remains a difficult task since the ‘device performance’ is actually made up of a multitude

of factors. Changing an operating parameter one way may be favorable for one factor but

adversely affect another factor.

3.1.1 Mass Transfer Prediction

In the proposed microdialysis chip, there are two flows separated by a

semipermeable membrane (Fig. 3.1) and is intended for in vitro use. Blood flows through

the reservoir channel while a saline solution flows through the perfusate channel.

Analytes in the reservoir fluid are dialyzed across the membrane, into the perfusion fluid.

36

Figure 3. 1: A side-view diagram showing the layer reservoir channels and the layer of perfusion

channels on opposite sides of a porous membrane [13]

The mass transfer coefficient, K0, is assumed to be constant over the diffusion path and

over time. The convective mass flux across the reservoir channel is given by

rrdCQmd −=& Equation 3.1

where Qr is the flowrate through the reservoir channel and Cr is the analyte concentration

in the reservoir solution. Rearranging Eq. 3.1 yields

r

rQ

mddC

&−= Equation 3.2

The convective mass flux of the perfusate is given by

dddCQmd −=& Equation 3.3

and another rearrangement yields

d

dQ

mddC

&−= Equation 3.4

37

where Qd is the flowrate through the perfusion channel and Cd is the analyte

concentration in the perfusate solution.

The mass flux across the membrane can also be given as

( )dACCKmd dr −= 0& Equation 3.5

where K0 is the membrane’s overall mass transfer coefficient (also referred to as the

membrane’s molecular permeability) and A is the diffusional area. By subtracting Eq. 3.4

from Eq. 3.2,

+−=−−=−

drdr

drQQ

mdQ

md

Q

mddCdC

11&

&& Equation 3.6

By substituting Eq. 3.5 into Eq. 3.6,

( ) ( ) dAQQ

CCKCCddr

drdr

+−−=−

110 Equation 3.7

Eq. 3.7 can then be rearranged into

( )( )

dAQQ

KCC

CCd

drdr

dr

+−=

−

− 110 Equation 3.8

By integrating Eq. 3.8 along the membrane diffusional area, Am

+−=

−

−

dr

m

indinr

outdoutr

QQAK

CC

CC 11ln 0

,,

,, Equation 3.9

where Cr,out and Cr,in are the outlet and inlet concentrations of the reservoir channel. Cd,out

and Cd,in are the outlet and inlet concentrations of the perfusion channel. Am is the

diffusional surface area. Qr and Qd are the flowrates through the reservoir and dialysate

channels. Cd,in is always zero for this work; that is, a saline solution, free of the analyte of

interest, enters the perfusion channel of the device. Cr,in and Cr,out are assumed to be

equals since the reservoir flowrate, Qr, is much greater than the perfusion flowrate, Qd. In

38

other words, the amount of analytes diffusing out of the reservoir solution is negligible

because it is constantly being replenished with more reservoir solution. Also, because Qr

is much greater than Qd, the fraction 1/Qr in Eq. 3.9 can be ignored. Therefore, Eq. 3.9 is

simplified to

−=

−

∞ QAK

C

Cm

out 11ln 0 Equation 3.10

where Cout is the dialysate concentration, C∞ is the reservoir concentration, and Q is the

perfusion flowrate. Eq. 3.10 can be rearranged to represent the extraction efficiency (also

known as “relative recovery”) as a function of perfusion flowrate

Q

AK

out

d

m

eC

CE

0

1−

∞

−== Equation 3.11

where a high extraction efficiency is achieved when (K0Am) >> Q.

3.1.2 Fluid Pressure and Resistance

Balancing the hydraulic pressures in the dual-compartment microdialysis system

is important to ensure that diffusion is the primary mode of mass/analyte transport,

instead of convection. If the hydraulic pressure in the reservoir channel is much greater

than that of the perfusion channel, the dialysate concentration will increase by having

blood plasma cross the membrane and enter the perfusion channel. However, this may

also cause large particles in the reservoir solution, mainly blood cells, to become lodged

or lyse as it tries to squeeze into the pores. On the other hand, if the hydraulic pressure in

the perfusion channel is much greater than that of the reservoir channel, perfusate may

39

flow across the membrane, thereby diluting the reservoir solution and reducing the

dialysate sample volume.

The pressure drop for a viscous incompressible fluid flowing through a constant

cross-section is a function of the channel geometry and flowrate, which is given by,

QRP =∆ Equation 3.12

where ∆P is the pressure drop, Q is the fluid flowrate, and R is the geometric resistance

term.

For a rectangular channel, the resistance term is given by

1

,...5,3,1553 2

tanh1192

112

−∞

=

−= ∑n

rectH

Wn

nW

H

WH

LR

ππ

µ Equation 3.13

where µ is the fluid dynamic viscosity, L is the length of the channel, W is the length of

the long edge of the channel cross-section, and H is the length of the short edge of the

channel cross-section. For square, channels, W and H are equivalent.

For a circular channel, such as the cylindrical pores of the membranes or tubing,

the resistance term is given by

4

8

r

LRcirc π

µ= Equation 3.14

where r is the radius of the channel and L is the thickness of the membrane or length of

tubing.

40

3.2 Device Design and Fabrication

The microdialysis chip made up of three main components: a

polydimethylsiloxane (PDMS) layer for the reservoir channel, another PDMS layer for

the perfusion channel, and a polymer track-etch membrane (with either 100 or 400 nm

diameter pores) bonded in between (Fig. 3.2). The design and fabrication protocol created

for this thesis are a result of a series of many developmental iterations.

Figure 3.2: Exploded view of the three main components (right to left): PDMS layer for the reservoir

channel, a thin polymer membrane, and a PDMS layer for the perfusion channel.

3.2.1 General Design Considerations

According to Eq. 3.11, maximizing the diffusion area increases the extraction

efficiency. It is also important to consider the size of the overall device for ease of

manufacturing and to maintain the µTAS form factor. Using these constraints,

commercial track-etched membranes, 47 mm in diameter, were selected. The size of the

41

perfusion and reservoir channels were designed to maximize the diffusion area while

fitting within the membrane’s perimeter.

Instead of using a single-channel design, where the one channel would be several

millimeters wide, a multiple parallel-channel design has two main advantages: 1)

increased rigidity of the device, which is important because PDMS is very soft and

flexible, and 2) provides structural support for the fragile, thin membrane (~10 µm thick).

However, one must also consider the adverse affects of reducing channel width for the

sake of having multiple parallel channels, such as increasing hydraulic resistance and

shear stress. Since the perfusion flow is driven by a syringe pump, i.e. flowrate-

controlled, a large hydraulic resistance increases the pressure drop in the channel and

increases the chance for PDMS-membrane delamination. Also, high shear stresses are

known to cause cell lysis as well as platelet activation.

To ensure consistent and repeatable results from the microdialysis chip, the

perfusion channel and reservoir channel PDMS layers must be properly aligned with

respect to one another, so that the diffusion area does not vary from one produced device

to another (Fig. 3.3). The diffusion area is defined as areas where the perfusion channels

and reservoir channels overlap. Since each channel is only several hundred microns wide,

extra care must be taken in the alignment and bonding process. Small lateral

misalignments and/or rotational misalignments can reduce the diffusion area quite

drastically.

42

Figure 3.3: Demonstrating how improperly aligned channels can affect the diffusion area. Solid lines

represent one layer of parallel channels and the dotted lines represent the other layer. Left: proper

alignment results in full overlap. Center: even a small lateral shift can result in no overlap. Right: a

small rotational shift can also reduce overlap areas.

To overcome this problem, the reservoir channels are designed to be slightly

wider than the perfusion channels, making the alignment and bonding process more

forgiving. There are several advantages for making the reservoir channel width wider

than the perfusion channel: 1) the reservoir solution, blood, is sensitive to high shear

stresses, which is reduced by widening the channel, 2) the reservoir flowrate can increase

to further satisfy the Qr >> Qd assumption in Eq. 3.10, and 3) if the perfusion channel is

wider than the reservoir channel, diffusion becomes limited by the reservoir channel’s

width.

43

3.2.1.1 First design: no bifurcation

The first channel design consisted of a short inlet channel that led directly to a

series of parallel channels. A computational fluid dynamics (CFD) analysis (COMSOL

Inc., Burlington, MA) showed that the flow velocity is highest in the center channels and

quickly decreases for channels farther away, as shown the velocity field contour plot in

Fig. 3.4, where red denotes high velocity and blue denotes low velocity. Predicting

device performance is made difficult by not having uniform flowrates among the parallel

channels. It is also not an efficient way of using the diffusion areas, since there is

essentially no flow going through a majority of the channels farthest from the center.

Hydraulic resistance is a function of the path length, as shown in Eq. 3.13. Since the outer

channels in Figure 3.4 require a much longer detour to reach the outlet than the center

channels, where it is essentially a straight path, the flowrates cannot be expected to be

evenly distributed.

44

Figure 3.4G: CFD analysis of the non-bifurcating channel design. Fluid enters from the short

channel on the left and exits on the right. Most of the flow goes through the center channels, while the

outer channel have negligible flowrates.

3.2.1.2 Final Design: Bifurcating Tree

A bifurcating tree design is used to ensure that the flowrates in each of the parallel

channels are equal, as seen in the CFD analysis in Fig. 3.5. At each bifurcation stage, the

flowrate is divided equally into the next bifurcation stage. Inherent to the bifurcation

design, there are 2n channels, where n is the number of bifurcating stages. For this device,

there are 32 channels (n = 5).

Although both the perfusion and reservoir layers use the bifurcating tree design,

they are given a slightly different design from one another. Fig. 3.6 shows the two layers

properly aligned, in such a way that the long channels in the center have maximum

overlap areas. However, one can notice areas in the bifurcating tree sections where there

are no overlap. This staggered design minimizes the amount of interaction, whether it’s

diffusion or convection, in areas that make theoretical calculations more difficult.

45

Although minimized, it is impossible to avoid all overlap in the staggered areas without

having to make drastic design and manufacturing changes.

Figure 3.5: Bifurcating channel design: a CFD analysis showing a surface plot of the velocity field.

Red denotes high velocity and blue denotes low velocity. At each bifurcation stage, the flowrate splits

up equally. This is only a partial model due to computational constraints.

46

Figure 3.6: Stacked view of the perfusion layer (blue) aligned on top of the reservoir layer (red). The

staggered design in the bifurcating tree section is intended to minimize interaction between the two

layers, except for the main section in the center.

3.2.2 Photolithography and Soft Lithography

The microfluidic channels are created using photolithography and soft lithography

techniques. SU-8 negative photoresist (MicroChem, Boston, MA) is a UV light-sensitive

material used for its ability to create thick and high aspect ratio structures. When exposed

to UV light, negative photoresist become insoluble to photoresist developer, whereas

unexposed portions are dissolved by the developer. Using the dark field masks shown in

Fig. 3.7 and a mask aligner (EVG620, EV Group, Austria), perfusion and reservoir

structures were created on silicon wafers. The schematic of the procedure is shown in

Fig. 3.8 and the full recipe is given in Tables 1 and 2.

The channels in the bifurcating trees for the perfusion and reservoir masks are

400µm wide. The widths of the main channel are 400 and 600 µm for the perfusion and

47

reservoir channels, respectively. The length of the main section is 25 mm long for both

layers. The recipe in Table 1, using SU-8 2025, creates a layer of photoresist 30 µm thick

while the recipe in Table 2, using SU-8 2150, creates a layer of photoresist 130 µm thick.

Figure 3.7H: Dark-field masks for photolithography. Left: Perfusion mask. Right: Reservoir mask.

Figure 3.8: Soft-lithography steps used to create microfluidic channels in PDMS.

48

Table 1: Photolithography recipe for 30 micron thick Perfusion Channel

Perfusion Channel - 30 micron thickness

# Step Description Time

Soak silicon wafer in acetone solution 10 min

Soak silicon wafer in isopropyl alcohol (IPA) solution 10 min

Soak silicon wafer in deionized (DI) water 10 min

Rinse under running DI water 1 min

Blow dry with filtered nitrogen or filtered air 1 min

1 Cleaning Procedures

Bake in vented oven at 200C 30 min

2 Spin Coating

SU-8 2025, 500 RPM for 5 sec @ accl. 100 RPM/sec, then 2875 RPM for 30 sec @ accl. 300 RPM/sec ---

Place on hot plate at 65C 2 min 3 Softbake

Place on hot plate at 95C 5 min

4 Exposure Set exposure dose to 300

mJ/cm^2

Place on hot plate at 65C 1 min 5 Post-exposure Bake


6 Develop Soak in SU-8 developer solution, agitate 5 min

7 Rinse Rinse in IPA ---

Table 2: Photolithography recipe for 130 micron thick Reservoir Channel

Reservoir Channel - 130 micron thickness

# Step Description Time

Soak silicon wafer in acetone solution 10 min

Soak silicon wafer in isopropyl alcohol (IPA) solution 10 min

Soak silicon wafer in deionized (DI) water 10 min

Rinse under running DI water 1 min

Blow dry with filtered nitrogen or filtered air 1 min

1 Cleaning Procedures

Bake in vented oven at 200C 30 min

2 Spin Coating

SU-8 2150, 500 RPM for 10 sec @ accl. 100 RPM/sec, then 3000 RPM for 30 sec @ accl. 300 RPM/sec ---

Place on hot plate at 65C 6 min 3 Softbake


4 Exposure Set exposure dose to 250

mJ/cm^2

Place on hot plate at 65C 5 min 5 Post-exposure Bake


6 Develop Soak in SU-8 developer solution, agitate 16 min

7 Rinse Rinse in IPA ---

49

The photolithography step creates the “master,” a negative mold comprised of

photoresist on a silicon wafer from which many PDMS molds can be made from [92].

The master is placed inside a petri dish, with the photoresist-side facing up. PDMS (Dow

Corning Sylgard 184, Dow Corning, Midland, MI) molds are created by mixing the base

and curing agent at a ratio of 10:1 by mass, then pouring the mixture into the petri dish.

This can then be allowed to cure at room temperature overnight or in a 600C oven for 2

hours to solidify. Cured PDMS is cut and peeled from the master mold and inlet/outlet

access holes are punched out with an 18G flat-tipped needle so that Intramedic PE-10

polyethylene tubing (Becton Dickinson, Franklin Lakes, NJ) can be inserted with a snug

fit. Once the tubing is inserted, a fast-curing sealant is applied around the base of the

tubing to prevent leakage and accidental removal.

3.2.3 Bonding to membrane

The bonding portion of the production process is the most critical, yet most

difficult, step. Several experiments were performed to find the most effective bonding

method between the polycarbonate (PC) track-etched membrane (Fig. 3.9) and PDMS

pieces. No method can be declared a decisive winner because each offers benefits as well

as drawbacks.

3.2.3.1 Thermal

Putting the two materials together and placing it in a 1600C to 180

0C oven for 5 or

more hours resulted in a very strong, non-reversible bond. Unfortunately, extreme

wrinkling of the membrane was observed after the bonded device is removed from the

50

oven. Membrane wrinkling is one of the main manufacturing problems because it

typically leads to partial or complete blockage of the channels, rendering the entire device

unusable. As the temperatures of the PDMS layers and PC membrane rises in the oven,

PDMS expands more than the membrane because of its larger thermal expansion

coefficient. Eventually, this is followed by the two materials being permanently bonding

to one another, at their disproportionately expanded state, once sufficient time and

temperature has been reached. As a result, the membrane takes on a “wrinkled”

appearance, creating peaks and valleys in the membrane, which are easily tall enough to

partially or completely obstruct the 30 µm tall perfusion channels. Although making

perfusion channels thicker than 30 µm can help with channel-blockage issues, that

change would also lower the extraction efficiency of the device by increasing the

diffusion length, thereby increasing the residence time the perfusate would require to

reach equilibrium with the reservoir channel concentration.

Figure 3.9: Commercial track-etched membranes. Left: a circular membrane, 47 mm in diameter,

held by a tweezer. Right: an SEM image of the cylindrical pores on the membrane. [93]

51

3.2.3.2 Thin film deposition

Although Whitesides et al. were able to irreversibly bond PDMS to materials such

as itself, glass, silicon, polyethylene, and polystyrene by simply exposing the surfaces to

oxygen plasma and bringing the surfaces into contact, it failed to work for materials such

as polyimide, PMMA, and polycarbonate [92]. Cremer et al. were able to produce an

irreversible bond between a thin film of titanium dioxide and PDMS by using

Whitesides’ oxygen plasma method.

Utilizing the works of Whitesides and Cremer, experiments were performed to see

if the PC membranes could first be coated with a thin film of titanium dioxide and then

bond it to PDMS, as Cremer had done in a similar manner. A thin film of pure titanium

was sputtered onto a PC membrane via magnetron DC sputtering (PVD75, Lesker,

Clairton, PA). Titanium oxidizes into titanium dioxide on its own when exposed to air,

but surface treating it with oxygen plasma also helps. Freshly cured PDMS and titanium

dioxide-coated PC membranes were treated with oxygen plasma using a variety of power

and time settings to find an optimal recipe. Once the membrane contacted PDMS, it was

left at room temperature over night with weights laying on top. These experiments

produced moderate to excellent bonding strength, similar to that of the thermal bonding

method but without the wrinkling issues. However, the bond disappears once the

membrane is exposed to water. Currently, it is not clear if the bond fails between PDMS

and titanium dioxide or between titanium dioxide and polycarbonate, but further research

into this method may find a way to overcome the water issue.

52

3.2.3.3 Epoxy Stamping

Of the methods mentioned thus far, the most effective method for bonding

membranes (where, in this case, “bonding” is referred to in the mechanical sense) to

PDMS is by using a biocompatible epoxy (Epo-Tek 301, EpoTek, Billerica, MA) as an

intermediate layer between PDMS and the membrane [94]. A major advantage for using a

“mortar” (e.g. glue, PDMS, or even brick mortar) to join surfaces together is that it is

forgiving for rough and imperfect surfaces, such as that found on a porous membrane.

Assuming the epoxy is capable of filling the micro-sized pores of the membrane, part of

its adhesive capability may be due to the bonding of epoxy on one end of a pore, to the

epoxy on the other end; thereby, interlocking the membrane. Because the microfluidic

channels embedded into the PDMS layer are only 30 µm and 130 µm thick for the

perfusion and reservoir channels, respectively, steps must be taken to prevent epoxy from

getting into the channels and causing partial or complete blockage. More importantly,

excess epoxy can spread onto the diffusion areas of the membrane, clogging the pores. In

addition to these problems, the strength of the bond is usually not very strong when only

a thin layer of epoxy is used.

Stamping consists of placing the bonding side of both PDMS layers onto a thin

layer of epoxy and joining the three layers together as shown in Fig. 3.10. Once joined,

the device is given 24 hours to cure to achieve full bonding strength. The simplest and

quickest method to create a thin layer of epoxy is to pour some epoxy onto a flat surface

and use a flat edge to spread the epoxy until a uniform thin layer is achieved. Using a

spin coating machine has the advantage of being able to create repeatable uniform

thicknesses, unlike the manual method of spreading a thin layer by hand. However, spin

53

coating is best used for slow curing adhesives because the spinning process can

completely drive off the solvent in epoxies before the bonding surfaces can come

together. For this reason, uncured PDMS is preferred for its longer curing time but seems

to suffer from a weaker bonding strength than epoxy.

Figure 3.10: Schematic for the epoxy stamping procedure. A) a small amount of epoxy is placed on

top of a clean glass slide; B) an object with a flat edge, such as another glass slide, is used as a

squeegee on the epoxy until a thin, uniform layer of epoxy remains; C) the first PDMS layer is placed

onto the thin layer of epoxy, with the channel side facing down; D) and E) a membrane is placed on

top of the epoxy-side of the first PDMS layer; F) steps A-C are repeated for the second PDMS layer

and aligned with the first layer under a dissection microscope.

3.3 Numerical Studies - Electric Circuit Model

In order to establish a starting baseline for channel geometry, membrane pore

size, tubing length, and flowrate parameters, a Matlab program was written to solve a

circuit diagram representing the experimental setup, as shown in Fig. 3.11. The objective

was to determine a set of conditions for which diffusion of analytes across the membrane

pores, from the reservoir channel to the perfusion channel, was the primary mode of

54

transport. In other words, convective flux was to be minimized and only in the direction

of reservoir-to-perfusate, if it exists at all.

In the circuit diagram, there are two flowrate sources: 1) the reservoir fluid

(blood) is driven by a pressure head generated by the CPB pump, represented by a

voltage source and 2) the perfusate (lactated Ringer’s solution) is driven by a syringe

pump at a specific flowrate, represented by a current source. The reservoir source

undergoes its first pressure drop due to the resistance in the reservoir channel’s inlet

tubing. Comparatively, the perfusion source is not followed by a resistor for the perfusion

channel’s inlet tubing since it is driven by a current source and its pressure drop does not

affect the rest of the circuit. The two nodal points on either side of the pore resistor

represent the pressure difference that determines the flowrate through the membrane

pores. An assumption is made that the pressure at the reservoir node is always greater

than or equal to the pressure at the perfusate node. Under this assumption, the perfusate

should not be able to enter the reservoir channel, which would dilute the reservoir

solution. This assumption is also necessary to provide enough known variables to solve

the set of linear equations described below; otherwise, since the pore’s resistance can

either be a function of the blood plasma’s viscosity or the Ringer’s solution’s viscosity,

depending on which direction fluid travels. This assumption can be verified by solving

for the entire circuit and checking to see if the reservoir node pressure is greater than or

equal to the perfusate node pressure, if not, that particular solution is invalid.

55

Figure 3.11: A circuit diagram representing the microdialysis chip. The reservoir side is given a

voltage source to represent the pressure source given by the CPB pump. The perfusate side is given a

current source to represent the predetermined flowrate put out by a syringe pump. Resistors

represent hydrodynamic resistance, which is a function of channel geometry and fluid viscosity.

Since convective flow through the pores can occur throughout the entire length of

the channel, the problem is simplified by dividing the pressure at the nodes in half when

calculating flowrate through the pores, thereby representing the average pressure over the

length of the channel. Finally, the perfusate and reservoir solutions experience pressure

drops due to their respective PDMS channels, where they eventually reach the end of the

device and into collection tubes, which are at atmospheric pressure. Although there is

tubing connected to the outlet ports of the device, this tubing is much shorter than the

inlet tubing and assumed to have negligible resistance.

56

Using Kirchhoff’s current law (KCL), which states that the sum of currents

flowing into a nodal point is equal to the sum of currents flowing out of the nodal point,

and Ohm’s law,

∆V = IRelec Equation 3.15

where ∆V is the voltage drop which is analogous to a pressure drop, I is the current

which is analogous to flowrate, and Relec is the electrical resistance which is analogous to

the pressure drop equation in Eq. 3.12 if the solutions are assume to behave as Newtonian

fluids..

At the ‘Reservoir Node’ (see circuit diagram in Fig. 3.11), applying KCL gives

pore

Rsrv

Rsrv

Tubing

RsrvsourceCPBQ

R

P

R

PP−−

−= ,

0 Equation 3.16

where PCPB,source is the pressure provided by the CPB circuit, PRsrv is the pressure at the

reservoir node, RTubing is the resistance in the tubing leading from where the reservoir

tubing connects with the CPB circuit to the reservoir-side of the device, RRsrv is the

resistance through the reservoir channels, and Qpore is the flowrate crossing the

membrane.

At the ‘Perfusate Node,’ applying KCL gives

Perf

Perf

PoresourcePerfR

PQQ −+= ,0 Equation 3.17

where Qperf,source is the syringe pump flowrate that is set by the user, PPerf is the pressure at

the perfusate node, and RPerf is the resistance through the perfusate channels.

The flowrate through the membrane is given by applying the hydraulic

equivalence of Ohm’s law,

57

( )Pore

PerfRsrv

PoreR

PPQ

−=

21 Equation 3.18

where the “½” refers to taking the average pressure difference between the channels, as

noted earlier.

For simplification, blood is assumed to be a non-Newtonian fluid in this analysis.

The blood flowrate entering the reservoir channel is given by applying the hydraulic

equivalence of Ohm’s law,

Tube

RsrvsourceCPB

sourceRsrvR

PPQ

−= ,

, Equation 3.19

The overall hydraulic resistance in the reservoir channel is given by applying Eq.

3.13,

1

,...5,3,1553 2

tanh1192

112

−∞

=

−= ∑

n Rsrv

Rsrv

Rsrv

Rsrv

ChanRsrvRsrv

RsrvH

Wn

nW

H

NHW

LR

ππ

µ Equation 3.20

where µBlood is the dynamic viscosity of blood at 35oC, L is the length for both the

perfusion and reservoir channels, WRsrv is the width of a single reservoir channel, HRsrv is

the height of the reservoir channels, and NChan is the number of channels. Without the

NChan term, the equation would only solve the resistance through a single channel.

The overall resistance in the perfusion channels is given by applying Eq. 3.13,

1

,...5,3,1553 2

tanh1192

112

−∞

=

−= ∑

n Perf

Perf

Perf

Perf

ChanPerfPerf

PerfH

Wn

nW

H

NHW

LR

π

πµ

Equation 3.21

where µLRS is the dynamic viscosity of lactated Ringer’s solution at room temperature,

WPerf is the width of a single perfusion channel, and HPerf is the height of the perfusion

channel.

58

The overall resistance in the membrane pores is given by applying Eq. 3.14,

( )[ ] PorePore

MembranePlasma

PoreND

TR

42

8

π

µ= Equation 3.22

where µPlasma is the dynamic viscosity of human blood plasma at 35oC, TMembrane is the

thickness of the membrane, DPore is the pore diameter give in Table 3, and NPore is the

number of pores available in the active diffusion area, Am. The SEM image in Fig. 3.9

(right) shows that the pores can be approximated as straight, uniform tubes.

The number of pores is a function of the pore density and the available diffusion

area given by the equation

( )LWNAN PerfChanPoremPorePore ρρ == Equation 3.23

where ρPore is the pore density which varies depending on the manufacturer’s

specifications (see Table 3). Am is a function of the perfusion channel’s width since the

perfusion channels are purposely designed to be narrower than the reservoir channels,

making perfusion widths the limiting factor.

The hydraulic resistance of the polyethylene tubing (Intramedeic PE-10, Becton

Dickinson, Franklin Lakes, NJ) connected to the reservoir inlet is given by,

( )4,

2

8

Tubing

TubingRsrvBlood

TubingD

LR

π

µ= Equation 3.24

where LRsrv,Tubing is the length of the reservoir inlet tubing and DTubing is the inner

diameter of the tubing.

59

Table 3: Whatman Nucleopore Polycarbonate Track-etched Membranes

Pore Size (micron)

Pore Density (pores/cm^2)

Membrane Thickness (micron)

0.05 6x10^8 6

0.08 6x10^8 6

0.1 3x10^8 6

0.2 3x10^8 10

0.4 1x10^8 10

0.6 3x10^7 10

0.8 3x10^7 9

3.3.1 Observing Trends from Matlab Code

Although the above equations are not used to calculate analyte extraction

efficiency, in this case, microdialysis performance is judged in terms of the perfusion

flowrate recovery (PFR). PFR is the ratio of the flowrate exiting the perfusion outlet to

the perfusion flowrate going in, given as

100,

, ×+

==sourcePerf

PoresourcePerf

Q

QQ

tenletFlowraPerfusionI

ateutletFlowrPerfusionOPFR Equation 3.25

where QPerf,source is the perfusion flowrate that is set by the syringe pump, and QPore is the

additional flowrate from blood plasma crossing over the membrane to the perfusion

channels due to some pressure differential. Under ideal conditions where there is no fluid

flux across the membrane, PFR equals 100% since there is no QPore contribution. If the

hydraulic pressure of the reservoir channel is much greater than the pressure of the

perfusion channel, extracellular fluid may cross the membrane and into the perfusion

channel, i.e. PFR > 100%, affecting Ed. In the reverse situation, where the perfusion

channel’s hydraulic pressure is much greater than the reservoir channel’s pressure, i.e.

PFR < 100%, meaning lactated Ringer’s solution crosses over to the reservoir channel,

60

which dilutes the analyte concentration in blood and affecting Ed as well.

In order to see how PFR is affected by operating parameters such as: CPB

pressure, perfusate flowrate, reservoir inlet tube length, and membrane pore size/density;

two parameters varied at a given time. Meanwhile, the remaining parameters are held at a

nominal value. Since commercial membranes are used in the devices, the membrane pore

size, pore density, and thickness are essentially non-customizable except for what is

already available in the product line. Because of this limitation, membrane selection is

important and will be used as the recurring variable in Fig. 3.12-3.14.

Fig. 3.12-3.14 show how small pore sized membranes have a very stable PFR

close to 100% across the span of the x-axis, while large pore sized membranes are very

sensitive to the x-axis parameter. Because the relationship between pore diameter and

pore resistance is 4

1

Pore

PoreD

R ∝ , the small pore sized membranes have such large

resistances that, relative to larger pore sized membranes, the flow on one side of the

membrane is less likely to be able to influence the flow on the opposite side. Pore

density has less of an impact, compared to the pore diameter, on overall resistance due to

its Pore

PoreRρ

1∝ relationship (where ρPore is the pore density), and is not referred to

explicitly when describing the membrane. A stable PFR around 100% across a wide

range of design and operating parameters is a quality that a robust device should have. It

means the device can operate predictably under varying conditions. Unfortunately, it can

also be an indication that the membrane’s pore resistance is too high (i.e. a completely

impermeable membrane would inherently always have a PFR of 100%). Therefore, a

compromise must be made between device robustness and analyte permeability.

61

There is negligible difference in PFR, between the 0.08 µm and 0.1µm pore size

membrane but a significant difference in PFR, between the 0.1 µm and 0.2 µm pore size

membrane (Fig. 3.12-3.14). Since there are no intermediate pore sizes available from the

manufacturer, the 0.1 µm membrane is a reasonable compromise between MWCO and

robustness. Fig. 3.12 shows a linear relationship between PFR and CPB pressure, where

the intersection point represents the chosen nominal value and large deviations from this

value dramatically affects PFR outcome. Meanwhile Fig. 3.13 and 3.14 show an

exponentially decaying relationships between PFR with respect to perfusion flowrate and

reservoir tubing length, where low perfusion flowrates and short reservoir tubing lengths

produce the largest deviations from 100% PFR. On the other hand, using high perfusion

flowrates is not necessarily the solution since it will lower Ed as seen in Eq. 3.11 .

0

50

100

150

200

250

300

0 20 40 60 80 100 120 140 160 180

CPB Pressure (mmHg)

Perfusion Flowrate Recovery %

.05 um pore

.08 um pore

0.1 um pore

0.2 um pore

0.4 um pore

0.6 um pore

0.8 um pore

Figure 3.12: Results from Matlab model: Perfusion flowrate recovery vs CPB Pressure, for various

pore sizes.

62

0

50

100

150

200

250

300

350

400

450

0 1 2 3 4 5 6 7 8 9

Perfusion Flowrate (ul/min)


.05 um pore

.08 um pore

0.1 um pore

0.2 um pore

0.4 um pore

0.6 um pore

0.8 um pore

Figure 3.13: Results from Matlab model: Perfusion flowrate recovery vs Perfusion flowrate, for

various pore sizes.

0

100

200

300

400

500

600

0 1 2 3 4 5 6 7 8 9

Reservoir Inlet Tubing Length (in)


.05 um pore

.08 um pore

0.1 um pore

0.2 um pore

0.4 um pore

0.6 um pore

0.8 um pore

Figure 3.14: Results from Matlab model: Perfusion flowrate recovery vs Reservoir inlet tubing

length, for various pore sizes.

Next, a similar analysis is performed using the Matlab program to observe the

effects of the reservoir channel height, CPB pressure, perfusion flowrate, and reservoir

63

tubing length on PFR, as shown in Fig. 3.15-3.17. The important information to extract

from these figures is the trend, rather than the PFR actual values, since the non-varying

parameters are assigned non-optimized values. In these figures, PFR is most stable when

the reservoir height is largest, for all three x-axis parameters. In this case, a reservoir

channel height of 110 µm exhibits very little PFR change, from one end of the x-axis to

the other, when compared to a reservoir channel height of 30 µm. A tall reservoir height

has the additional benefit of reducing the chances of damaging blood and further

activating the inflammatory response by reducing shear stress.

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

0 20 40 60 80 100 120 140 160

CPB Pressure (mm Hg)


Rsrv Height 30 um

Rsrv Height 50 um

Rsrv Height 70 um

Rsrv Height 90 um

Rsrv Height 110 um


reservoir channel heights.

64

0

1000

2000

3000

4000

5000

6000

7000

8000

0 1 2 3 4 5 6 7 8 9



Rsrv Height 30 um

Rsrv Height 50 um

Rsrv Height 70 um

Rsrv Height 90 um

Rsrv Height 110 um


various reservoir channel heights.

0

1000

2000

3000

4000

5000

6000

7000

0 2 4 6 8 10 12 14 16 18

Reservoir Inlet Tubing Length (in.)


Rsrv Height 30 um

Rsrv Height 50 um

Rsrv Height 70 um

Rsrv Height 90 um

Rsrv Height 110 um


length, for various reservoir channel heights.

65

In contrast to the previous figures showing the effects of reservoir heights, Fig.

3.18-3.20 show that a shallow perfusion channel height is more stable than a taller height,

and is preferred when designing for robustness. However, there is a limit to how shallow

a channel height can be before significant problems arise during the fabrication process.

Shallow channel heights suffer from a greater chance for epoxy to partially or completely

block channels during the epoxy stamping procedure.

0

100

200

300

400

500

600

700

800

900

0 20 40 60 80 100 120 140 160

CPB Pressure (mm Hg)


Perf Height 20 um

Perf Height 30 um

Perf Height 40 um

Perf Height 50 um

Perf Height 60 um


perfusion channel heights.

66

0

200

400

600

800

1000

1200

1400

0 1 2 3 4 5 6 7 8 9



Perf Height 20 um

Perf Height 30 um

Perf Height 40 um

Perf Height 50 um

Perf Height 60 um


various perfusion channel heights.

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 2 4 6 8 10 12 14 16 18

Reservoir Inlet Tubing Length (in.)


Perf Height 20 um

Perf Height 30 um

Perf Height 40 um

Perf Height 50 um

Perf Height 60 um


lengths, for various perfusion channel heights.

67

With the preceding Matlab simulation results and manufacturing constraints in

mind, design parameters were finalized for use with blood in a mock CPB circuit, shown

in Table 4. Although, theoretically, the objective is to maximize robustness and dialysis

performance, in reality, compromises in these areas must be made for manufacturing

reasons.

Table 4: Finalized Microdialysis Design for CPB integration

Perfusion Height 30 µm

Perfusion Width 400 µm

Reservoir Height 130 µm

Reservoir Width 600 µm

Channel Length 25 mm

Number of Channels 32

Membrane Pore Size 0.1 or 0.4 µm

Perfusion Flowrate (Syringe Pump) 4.1 µl/min

Membrane Bonding Method Epoxy

stamping

3.4 Microdialysis Experiments

In order to test the proof-of-concept of the proposed microdialysis device, bench-

top experiments were conducted using a syringe pump, instead of a CPB pump, and a

glucose/phosphate-buffered-saline (PBS) solution, instead of blood. Samples were then

collected from the device and analyzed for glucose. These bench-tops experiments helped

to establish protocols and techniques that were then used for the mock CPB circuit

experiments.

Before a device was to be used, it was exposed to oxygen plasma (power: 100 W,

time: 60 sec) for sterilization and to render the channel surfaces hydrophilic. Sterile DI

water is then used to completely fill all of the microchannels, including the tubing. This

68

step is vital to reduce the risk of a bubble lodging itself into a channel, thereby blocking

flow through that channel and disrupting the uniform flowrates across the 32 channels.

3.4.1 Experimental Setup: Glucose and PBS

Theoretically, changing perfusate and/or reservoir flowrates affect both the

pressure balance across the membrane and the extraction efficiency of the device (see Eq.

3.11) simultaneously. Bench-top experiments were conducted to find flowrates that

minimize convective flux across the membrane, while attempting to maximize analyte

recovery.

For these experiments, a variation of the final design (Table 4) was used: the

perfusion channel height was 20 µm, the reservoir channel height was 65 µm, the

membrane had a 0.4 µm pore diameter, the reservoir fluid was a ~200 mg/dl glucose/PBS

solution, and glucose-free PBS was used as the perfusate. The perfusate and reservoir

solutions were infused into the device via individually controlled syringe pumps. In this

case, the perfusion flowrate was held constant at 4 µl/min, while the reservoir flowrate

varied between 41 µl/min and 75 µl/min. Before connecting the reservoir syringe to the

device, a sample of the glucose/PBS solution was collected to be used as the reference

concentration, C∞. Once the device was connected and the syringe pumps were turned on

at the appropriate flowrates, the first samples were not collected until a 30 minute waiting

period had passed in order to allow the chemical and flow profiles to stabilize. This

waiting period was also used after every change made to the flowrate. Samples were

collected until there was at least 75 µl of solution in both collection tubes and the

collection time was recorded. Glucose concentration and volume measurements were

69

made at the reservoir and perfusate outlet. Glucose concentration was measured with a

biochemistry analyzer (YSI 2700 Select, YSI Life Sciences, Yellow Springs, OH) and

volume was measured using a pipette.

To verify the accuracy of the numerical simulations with experimental values, the

Matlab code used to simulate Fig. 3.11 was rewritten for the bench-top glucose/PBS

experiment with the following modifications: the reservoir channel became flowrate

driven via a syringe pump, instead of pressure driven by the CPB circuit; the reservoir

inlet tubing resistance is ignored due to the reservoir being current-sourced; the channels’

geometric resistances were modified to represent the changes made to the channel heights

and widths, as described in the previous paragraph; and all dynamic viscosities were that

of PBS since blood was not used. The revised circuit diagram is shown in Fig. 3.21.

Figure 3.21: A revised circuit diagram for the bench-top glucose/PBS experiments, based off of Fig

3.11, where the reservoir channel is driven by a syringe pump, instead of a CPB pump. Thus, the

reservoir inlet tubing resistance can be ignored and the reservoir inlet is now represented with a

current source.

70

3.4.2 Results and Discussion: Glucose and PBS

Results for the experimental and theoretical volume recoveries, as a function of

reservoir flowrate, are shown in Fig. 3.22, where volume recovery is defined as the

volume measured at the outlet of either the perfusion channel (PERF), or reservoir

channel (RSRV), divided by the volume of fluid infused by the respective syringe pump,

which is determined by multiplying the flowrate by the collection time. A volume

recovery greater than 100% implies that more volume exits that particular channel than

was expected, and vice versa. As reservoir flowrate increases, the hydraulic pressure

within the reservoir channels also increases, driving more and more reservoir solution to

cross the membrane into the perfusion channel. As a result, the reservoir volume recovery

decreases. Intuitively, the perfusion volume recovery increases as a result. Linear

regression trendlines for perfusion and reservoir volume recovery data show an

intersection point when the reservoir flowrate is 50 µl/min and the perfusate flowrate is 4

µl/min, at which point both channels have ~100% volume recovery. Theoretically, this

point suggests that there is very little convective flux across the membrane, from either

direction.

Despite the appearance that the theoretical values for the reservoir volume

recovery matches closely to its corresponding experimental values (Fig. 3.22, solid and

hollow square data points) and that the experimental perfusion volume recovery appears

to be quite different than its predicted values, this outcome is partially due to the fact that

the reservoir flowrate was significantly greater than the perfusion flowrate. For example,

4 µl/min “error” between the experimental and theoretical reservoir outlet flowrate is a

relatively small difference compared to its original value ranging between 41 µl/min and

71

75 µl/min). How ever, when that additional 4 µl/min crosses into the perfusion channel, it

doubles the original flowrate of 4 µl/min. Therefore, a better methodology for evaluating

the accuracy of the numerical model would be to run both channels at similar flowrates.

Volume Recovery vs Reservoir Flowrate

20

40

60

80

100

120

140

160

35 45 55 65 75 85

Reservoir Flowrate (uL/min)

Volume Recovery %

Perf, Exper.

Rsrv, Exper.

Perf, Theor.

Rsrv, Theor.

Linear (Rsrv,

Exper.)

Linear (Perf,

Exper.)

Linear (Perf,

Theor.)

Linear (Rsrv,

Theor.)

Figure 3.22: Theoretical (hollow) and experimental (solid) Volume Recovery values for perfusion

(diamond) and reservoir (square) outlets, versus varying reservoir flowrates.

Glucose concentration recovery as a function of reservoir flowrate is shown in

Fig. 3.23, where recovery is defined as the outlet concentration divided by the reference

concentration, C∞. The figure shows the outlet concentration recovery from both channels

overlapping one another throughout the full range of flowrates tested. Both the perfusion

and reservoir fluids reach very similar glucose concentrations throughout the entire range

of reservoir flowrates, despite the direction of convective flux across the membrane. The

72

assumption that the two solutions are fully mixed by the time it exits the device by

verifying that,

totalinitialtotalinitialrsrvfinalrsrvfinalperffinalperffinal CmCmCm ,,,,,,&&& =+ Equation 3.26

where, perffinalm ,& , rsrvfinalm ,

& , and totalfinalm ,& are the glucose mass flow rates from the

perfusion outlet, reservoir outlet, and the total from the perfusion and reservoir inlet,

respectively. perffinalC , , rsrvfinalC , , and totalinitialC , are the glucose concentration values from

the perfusion outlet, reservoir outlet, and the total from the perfusion and reservoir inlet,

respectively.

From solving Eq. 3.26, it was shown that the two solutions were indeed fully

mixing while inside the device, most likely due to the larger 0.4 µm membrane pore size

that was used. The slight dilution of the glucose/PBS reservoir solution is not expected to

be a concern as long as the mass flow rate of the reservoir solution is significantly greater

than that of the perfusate solution.

Based on the numerical studies, shown in Fig. 3.12-3.14, the effect that flowrate

has on volume recovery can be decreased by using membranes with smaller pore sizes.

While this may aid in reducing large changes in volume recovery, it may also reduce

perfusate analyte recovery.

73

Glucose Recovery vs Reservoir Flowrate

50

60

70

80

90

100

110

120

130

140

150

30 40 50 60 70 80 90

Reservoir Flowrate (uL/min)

Glucose Recovery %

PERF, concent.

RSRV, concent.

Linear (RSRV, concent.)

Linear (PERF, concent.)

Figure 3.23: Glucose concentration recovery for perfusion and reservoir channels, for varying

reservoir flowrates. Data shows that both channels end up with near-identical concentrations for a

wide range of flowrates, causing the data points to overlap one another.

3.4.3 Introduction: Blood with Mock CPB Circuit

The microdialysis device, as described in Table 4, was used in a mock CPB

circuit to test the recovery performance for the complements C3a, C4a, and C5a in human

blood. Experiments were conducted under the supervision of Dr. Akif Undar, Director of

the Pediatric Cardiac Research Laboratories at Hershey Medical Center (Hershey, PA).

Two devices were tested on the same day, but separately: the first had a membrane pore

diameter of 0.1 µm and the other had a 0.4 µm diameter. The devices were otherwise

identical.

74

3.4.3.1 Experimental Setup: Blood with Mock CPB Circuit

A mock in vitro CPB circuit was primed by a perfusionist, where packed red

blood cells (PRBCs) are hemodiluted with lactated Ringer’s solution to obtain a

hematocrit level of 26% and pumped through the circuit at 500 ml/min at an arterial

circuit pressure of 100 mmHg. The Hershey Medical Center’s blood bank provided

PRBCs as a substitution for whole blood due to the limited availability of whole blood

for non-medical, non-emergency usage. The “packed cells” are prepared by removing

platelets, plasma, and sometimes white blood cells from whole blood. Although PRBCs

contain little coagulation factors, 4 Units/ml of heparin was added to the circuit to

simulate a real CPB circuit as accurately as possible. A heat exchanger maintained the

blood at normothermic conditions. The perfusionist monitored and controlled blood pH-

levels by supplying appropriate blood-gases

Prior to connecting the microdialysis devices to the CPB circuit, both the

perfusion and reservoir channels were infused with a filtered 0.5% w/v solution of PBS

and bovine serum albumin (BSA) at 60 µl/min and 4 µl/min, respectively, for 30 minutes.

BSA is commonly used to minimize surface adsorption of the analyte to exposed areas

such as the channel walls and membrane surface [95, 96].

The device’s reservoir inlet tubing was then connected to the circuit at a sampling

manifold located downstream of the arterial port of the membrane oxygenator, as shown

in Fig. 3.24. The device’s perfusion inlet tubing was connected to a syringe filled with

lactated Ringer’s solution, which was driven by a syringe pump. The perfusion flowrate

was set to 4.1 µl/min while the reservoir flowrate was determined to be 40 µl/min,

according to timed volume measurements. For the first 45 minutes, the fluid exiting the

75

device was not collected for analysis since this contained the PBS-BSA solution initially

infused into the device. Once this waiting period had passed, reservoir outlet and

perfusate outlet samples were collected in separate 1.5 ml microcentrifuge tubes for 15

minutes, every 15 minutes, for 1.5 hours (i.e. 6 samples).

At the half-way mark of each 15 minute sampling period, a 1 ml blood sample

was collected from a different sampling port downstream of the membrane oxygenator.

This blood sample provided a snapshot of analyte concentrations in the blood before it

enters the reservoir channel, thereby providing a reference point to compare how much

the reservoir solution was being diluted during dialysis, if at all. Collecting this blood

sample at the 7 min. 30 sec. mark provided an estimate of the average analyte

concentration during each 15 minute sampling period, in case C3a, C4a, and C5a levels

fluctuated over time.

Collected samples were stored on ice, until the end of the experiment, when they

were snap-frozen at -80OC. Analysis was performed by Hershey Medical Center using a

commercially available anaphylatoxin cytometric bead kit (BD Biosciences, San Jose,

CA).

76

Figure 3.24: The setup for the mock CPB circuit experiments. A relatively small quantity of blood

flow is routed to the reservoir channel of the microdialysis device, via a Luer connection at the

sampling manifold on the arterial side of the oxygenator.

77

3.4.3.2 Results and Discussion: 0.1 µm membrane

A two-tailed paired t-Test was conducted on the data, where the null hypothesis,

H0, states that the two sample means are equal in concentration or relative recovery. The

statistical significance value, α, used is 0.05.

For the 0.1 µm device, the average C3a, C4a, and C5a concentration recoveries

are shown in Fig. 3.25 for the perfusion outlet, reservoir outlet, and CPB sample. The

graph shown in Fig. 3.26 uses the same data as Fig. 3.25 but converts it to relative

recovery (equivalent to extraction efficiency, Ed) for a quicker evaluation of device

performance, simply by dividing the perfusion or reservoir outlet concentration with the

CPB circuit concentration.

For C3a in the 0.1 µm device (Fig. 3.25, left), the perfusion channel appeared to

reach an equilibrium point with the reservoir channel but at the expense of a diluted

reservoir channel, as demonstrated by the higher C3a concentration from the CPB circuit.

Using the CPB circuit concentration as reference, the relative recovery for the perfusion

outlet and reservoir outlet are 79% and 74%, respectively (Fig. 3.26, left).

For C4a in the same device (Fig. 3.25, center), relative recovery for C4a in the

perfusion and reservoir outlets were 75% and 56%, respectively (Fig. 3.26, center).

However, the perfusion channel resulted in unexpectedly higher relative recovery than

the reservoir channel.

The graph for C5a (Fig. 3.25, right) show yet another difference in device

performance. Relative recovery for C5a in the perfusion and reservoir outlets were 70%

and 93%, respectively (Fig. 3.26, right).

78

By looking at Fig. 3.26 as a whole, one notices that the relative recovery for the

perfusion outlet varies only slightly, between 70-79%, while the reservoir outlet varies

more widely between 74-93%. Unfortunately, it is not yet clear whether the consistency

in the perfusion outlet’s relative recovery is coincidental and, if not, why it would happen

while the reservoir outlet recovery fluctuates significantly more. It is also not clear why

C3a concentration from the perfusion and reservoir outlets were able to equilibrate during

dialysis, but C4a and C5a concentrations were not. One theory is that the difference in

molecular structures of the complements affects its permeability through the pores.

Figure 3.25: Analyte concentration for the 0.1 µm membrane device: (left) C3a, (center) C4a, and

(right) C5a. Data represents an average of 6 data points over a 1.5 hour period. A two-sample paired

t-Test was performed, where H0 = two means are equal. The asterisk (*) represents a statistical

significance level, α<0.05.

79

Figure 3.26: Relative recovery for the 0.1 µm membrane device: (left) C3a, (center) C4a, and (right)

C5a. Data represents an average of 6 data points over a 1.5 hour period. The asterisk (*) represents a

statistical significance level, α<0.05.

The p-values for a two-tailed paired t-Test and correlation coefficient values for

Fig. 3.25 and 3.26 are summarized in Table 5 and 6, respectively. According to these two

tables, the noticeable differences in the paired recovery values of the 0.1 µm membrane

device is unlikely to be coincidental and for the most part, the paired recovery values

show medium to high positive correlation, and surprisingly, with low and negative

correlations as well in C5a. Essentially, no statistical significance can be found for the 0.1

µm device.

80

Table 5: 100 nm membrane: p-values, pairwise t-test. Blue/bold values denote acceptance of the null

hypothesis.

Perf/Rsrv Perf/CPB Rsrv/CPB Perf_RR% / Rsrv_RR% C3a 0.020 0.000 0.000 0.012 C4a 0.004 0.004 0.001 0.001 C5a 0.000 0.000 0.070 0.001

Table 6: 100 nm membrane: correlation coefficient

Perf/Rsrv Perf/CPB Rsrv/CPB Perf_RR% / Rsrv_RR% C3a 0.912 0.830 0.654 0.859 C4a 0.941 0.797 0.745 0.761 C5a -0.142 0.727 0.128 0.465

3.4.3.3 Results and Discussion: 0.4 µm membrane

The 0.4 µm device appeared to have yielded more consistent and overall better

performance than the 0.1 µm device. From Fig. 3.27, one can clearly see more mean

concentrations being comparable to one another, evidence of good recovery performance

for the perfusion and reservoir channels. The reservoir outlet mean relative recoveries for

C3a and C5a, shown in Fig. 3.28, are close to 100% (105% and 106%, respectively),

whereas the reservoir outlet mean relative recovery for C4a is slightly greater, at 118%.

81

Figure 3.27: Analyte concentration for the 0.4 µm membrane device: (left) C3a, (center) C4a, and

(right) C5a. Data represents an average of 6 data points over a 1.5 hour period. A two-sample paired

t-Test was performed, where H0 = two means are equal. The asterisk (*) represents a statistical

significance level, α<0.05.

Figure 3.28: Relative recovery for the 0.4 µm membrane device: (left) C3a, (center) C4a, and (right)

C5a. Data represents an average of 6 data points over a 1.5 hour period. The asterisk (*) represents a

statistical significance level.

The p-values for a two-tailed paired t-Test and correlation coefficient values for

Fig. 3.27 and 3.28 are summarized in Table 7 and 8, respectively. According to these two

82

tables, the noticeable differences in the paired recovery values of the 0.4 µm membrane

device is unlikely to be coincidental and for the most part, the paired recovery values

show medium to high positive correlation in most cases, and similar to C5a in the 0.1 µm

device, the C5a results here had low negative correlations as well. In both cases, Fig. 3.31

in the next section demonstrates these results. The changes in concentration of C5a is so

minimal and seemingly noisy that one cannot expect a strong correlation.

Table 7: 400 nm membrane: p-values, pairwise t-test. Blue/bold values denote acceptance of the null

hypothesis.

Perf/Rsrv Perf/CPB Rsrv/CPB Perf_RR% / Rsrv_RR% C3a 0.089 0.004 0.210 0.092 C4a 0.002 0.000 0.002 0.001 C5a 0.610 0.821 0.278 0.515

Table 8: 400 nm membrane: correlation coefficient

Perf/Rsrv Perf/CPB Rsrv/CPB Perf_RR% / Rsrv_RR% C3a 0.587 0.836 0.592 0.486 C4a 0.944 0.987 0.956 0.871 C5a -0.008 0.839 -0.253 -0.341

3.4.3.4 Time Course Data

The time course data is given in Fig. 3.29-3.31 in order to observe the standard

deviations for a given sample measured using a cytometric bead assay. Although both the

0.1 µm and 0.4 µm devices follow the trend of the CPB concentration over time, albeit

roughly at times, the 0.4 µm device clearly has a better extraction efficiency throughout

83

the time course. The standard deviations, as denoted by the error bars, remain fairly

consistent for the C3a and C4a plots, Fig. 3.29 and Fig. 3.30, respectively. However, the

C5a plot for the 0.1 µm device had a significant jump in standard deviation at t = 15 min.

and t = 75 min., as seen in Fig. 3.31. In the same figure, the 0.4 µm device had a single

inconsistently large standard deviation in the reservoir outlet at the 75 minute marks as

well. The fact that, at the 75 minute mark, the reservoir outlets for both devices

experienced similar results (large standard deviation) does not seem like a coincidence.

Perhaps some form of human error, such as mishandling the samples during collection,

could have caused this outcome.

84



85

Figure 3.3 1: Time course data with error bars representing 2 standard deviations for C5a. (Top)

Zoomed out to see full extent of error bars at 15 and 75 min. (Bottom) Zoomed in.

86

Chapter 4 - Conclusions and Future Work

It appears that the larger pore-sized device resulted in an overall better performing

microdialysis device even though there was an initial concern about the increased risk of

convective flux across the membrane. Although the pore resistance in the 0.1 µm device

was calculated to be 51 times greater than the 0.4 µm device, there seems to be less

reservoir solution dilution in the larger pore-sized device. Another significant benefit

from using the larger membrane pore size is the increased perfusate extraction efficiency.

If whole blood or human patients are used in the experiment, other problems may

develop and have to be accounted for, such as biofouling of the membrane from platelet

activation and influences of blood temperature on device performance. When biofilm

forms on the membrane surface, it can block pores and decrease membrane permeability.

During an open-heart procedure, surgeons will typically cool the patient’s body to

intentionally induce hypothermia and eventually bring them back to normothermic

conditions. This large temperature change will affect the blood viscosity and therefore,

the hydraulic pressure within the microdialysis device, but can be remedied by adjusting

the perfusion flowrate and adjusting calibration values for C∞ as needed.

87

In the future, one major change in the microdialysis setup would be to use a

peristaltic pump, in between the CPB circuit sampling manifold and the reservoir inlet

tubing of the device. The use of a peristaltic pump will improve consistency by changing

the reservoir channels mode of transport from pressure-based to flowrate-based. During

an actual CPB procedure, the arterial circuit pressure may vary from patient to patient,

vary over time, and vary depending on the blood viscosity, which itself can vary due to

hematocrit and temperature. A peristaltic pump will give the microdialysis operator more

control of the flow conditions within the device. During mock CPB circuit experiments, it

was also noted that the pressure gauges were very sensitive to the placements of the

circuit tubing and sampling manifold, since this inherently affects the head pressure in the

circuit. Therefore, relying on the circuit pressure readings to determine expected reservoir

flowrate may yield erroneous predictions.

The fabrication procedure should also be improved upon; more importantly, a

more reliable bonding method is needed. Currently, the benefit from using a low

viscosity epoxy is the ability to create a thin layer of epoxy for stamping, which

minimizes additional diffusion distances required for the analyte to cross over from the

reservoir channel to the perfusion channel. However, this low viscosity property also

increases the chances of the epoxy spreading into the channels as well as spreading to

membrane surfaces beyond the template dictated by the PDMS channels. Since each of

the perfusion channels are only 400 µm wide, the available diffusion area may decrease

significantly. Furthermore, the

Due to the epoxy’s transparent nature, especially since its thickness is only tens of

microns, it is difficult to visually see when epoxy spreads out beyond the intended

88

membrane areas or into the channels themselves. The only method to perform quality

control checks is to perform microdialysis experiments (e.g. dialyzing glucose) on a large

set of devices, of the same design, and compare the extraction efficiency results. If the

variance is small, poorly made devices can be spotted easily and the rest would be

deemed acceptable for actual CPB usage. If the variance is large, it may be difficult to

distinguish which devices are not built to specifications.

To improve the bonding performance, further research into dry bonding

techniques is necessary. Since titanium-dioxide-coated polycarbonate membranes have

been shown to provide excellent bonding strength in air, but not when exposed to liquids,

other combinations of thin film material and membrane material may overcome this

limitation.

Compared to currently available, commercial microdialysis probes, this proposed

device has better extraction efficiency performance, especially at high flowrates (~4

µl/min). Its in vitro design makes it less invasive for the patient and reduces the risk of

infections, whereas microdialysis probes are designed to be placed directly on tissue or in

ECF. Although it is beyond the scope of this project, this microdialysis device is intended

to work in conjunction with a microimmunoassay module (also a µTAS device) that can

continuously track the changing inflammatory protein markers, such as that created by

Yang et al. [16, 97] and currently being investigated by Sasso et al. [98-100]. The

microdialysis chip would therefore serve to continuously prepare a cell-free solution that

contains similar levels of analyte concentration as that in the blood.

89

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95

Appendix A: Preliminary Experiments

Preliminary experiments were conducted using channels with simple single-

channel devices. These were done as proof-of-concept tests of various bonding methods

and as practice for sample collection and analysis techniques. The PDMS device

consisted of a single channel, 2 mm wide, 12 mm long, and 100 µm deep, for both the

reservoir and perfusion sides. A polycarbonate membrane with 100 nm pore sizes were

used. A syringe pump was used to control each of the channel’s flowrate.

Figure A. 1: Various orientations of the channels: (left) reservoir channel is directly over perfusion

channel; (middle) reservoir channel is perpendicular to perfusion channel; and (right) the two

channels are offset laterally by one-half the channel width. Arrows denote direction of flow.

96

First, the “parallel” configuration was used, as shown in Fig. A.1, where both

channels are aligned directly over one another. The reservoir solution consisted of a 1.27

g/l glucose/PBS mixture and pumped at a flowrate 40 µl/min while the perfusate solution

was pumped at various flowrates, as shown in Fig. A.2.

0

10

20

30

40

50

60

70

80

90

100

0 1 2 3 4 5 6 7 8 9

Perfusion Flowrate (uL/min)

Relative Recovery %

Experimental

Theoretical

Equilibrium

Figure A. 2: Glucose recovery at the perfusion outlet shown in Fig. A.1 (left), “parallel”

configuration.

The theoretical relative recovery values in Fig. A.2 were computed using the

membrane permeability value, K0, determined by KaleidaGraph’s (Synergy Software,

Reading, PA) regression analysis of the experimental data itself. Thus, the resulting K0

value is assumed to be only relevant to each own respective data set. The result clearly

shows that the change in perfusion flowrate has little effect on the relative recovery,

perhaps signifying that the two solutions are crossing through the membrane from their

respective channels and mixing with one another. However, the two concentrations do

not reach the theoretical equilibrium concentration value (shown in Fig. A.2), which

97

assumes that both solutions have infinite time for analytes to cross the membrane. One

should also note that, under this configuration, the membrane does not remain flat and

parallel to the plane where the two PDMS layers come in contact. In fact, it bows in the

shape of a “U” due to the relatively wide and unsupported width of the channel. This

results in an unexpected change in effective channel depth, thereby affecting the

hydraulic pressure within the channel. This configuration also places the inlet and outlet

holes of each channel, directly over the other channel. This does not allow the flow to

stabilize first, before diffusion across the membrane is supposed to occur. In order to

remedy these two problems, alternative alignment configurations were used, such as the

“cross” and “shifted parallel” configurations shown in Fig. A.1 (middle and right).

In the cross configuration, the two channels are oriented perpendicular from one

another, thereby decreasing the diffusion area, but also limiting the amount of bowing of

the membrane. This setup also allows the flow to stabilize in its respective channel before

the fluid reaches the diffusion area. The theoretical and experimental values were

calculated using the same method as in the parallel configuration and shown in Fig. A.3.

As one can see, the relative recovery values are significantly lower than that of the

parallel configuration due to the decreased diffusion area. However, the experimental

values do follow an exponential trend, as noted by the agreement with the expected

values in Fig. A.3. The plot also demonstrates that bulk mixing is not occurring or is

negligible.

98

0

10

20

30

40

50

60

70

80

90

100

0 1 2 3 4 5 6 7


Relative Recovery %

Experimental

Theoretical

Equilibrium

Figure A. 3: Glucose recovery at the perfusion outlet shown in Fig. A.1 (middle), “cross”

configuration.

Finally, the shifted parallel configuration was used also to limit bowing across the

width of the membrane, by shortening the width of the diffusion area, and to limit the

deleterious effects of the inlet and outlet holes in the PDMS channel to be so close to the

diffusion area. Once again, the experimental values are shown to follow an exponential

trend and does not seem to experience mixing between the two channels, as shown in Fig.

A.4.

99

0

20

40

60

80

100

120

0 2 4 6 8 10

Recovery %


Experimental

Theoretical

Equilibrium

Figure A. 4: Glucose recovery at the perfusion outlet shown in Fig. A.1 (right), “shifted parallel”

configuration.

100

Appendix B: Matlab Code

clear all; display(' '); display(' '); display(' ');display(' '); display(' '); display(' '); display('********************************************************** '); % display(datestr(now)); display('********************************************************** '); display(' '); Width_Blood_um = input('Width of blood channel (um): '); Width_Blood_m = Width_Blood_um .* 10^-6; length_Width_Blood = length(Width_Blood_m); Height_Blood_um = input('Height of blood channel (um): '); Height_Blood_m = Height_Blood_um .* 10^-6; length_Height_Blood = length(Height_Blood_m); Width_Perfus_um = input('Width of perfus channel (um): '); Width_Perfus_m = Width_Perfus_um .* 10^-6; length_Width_Perfus = length(Width_Perfus_m); Height_Perfus_um = input('Height of perfus channel (um): '); Height_Perfus_m = Height_Perfus_um .* 10^-6; length_Height_Perfus = length(Height_Perfus_m); Length_mm = input('Length of channel (mm): '); Length_m = Length_mm .* 10^-3; N = input('Number of channels: '); Tube_rsrv_inlet_in = input('What is the length of PE-10 tubing for the Reservoir Inlet (in): '); Tube_rsrv_inlet_m = Tube_rsrv_inlet_in.*.0254; % convert in to meters length_Tube = length(Tube_rsrv_inlet_m); display(' '); Q_perf_uLmin = input('What is perfusion flowrate (uL/min): '); Q_perf_in = sym(Q_perf_uLmin.*1.667e-11); length_Q_perf = length(Q_perf_in);

101

P_CPB_mmHg = input('What is the CPB pump pressure into reservoir (mmHg): '); P_CPB_Pa = sym(P_CPB_mmHg.*133.3); length_P_CPB = length(P_CPB_Pa); Pore_diam_um = input('Pore size (um): (0.05, 0.08, 0.1, 0.2, 0.4, 0.6, or 0.8) = '); length_Pore = length(Pore_diam_um); % FOR LOOP in order of importance for analysis % Pore Size >> Blood Height >> Blood Width >> Perfus Height >> Perfus Width >> % Tube L >> CPB Press >> Q_perfus % END string_varying_variables = input('Note: ','s'); for index_Pore = 1:length_Pore for index_Height_Blood = 1:length_Height_Blood for index_Width_Blood = 1:length_Width_Blood for index_Height_Perfus = 1:length_Height_Perfus for index_Width_Perfus = 1:length_Width_Perfus for index_Tube = 1:length_Tube for index_CPB = 1:length_P_CPB for index_Q_perfus = 1:length_Q_perf

ResistCalc_AUTO(Width_Blood_m(index_Width_Blood),... Height_Blood_m(index_Height_Blood),... Width_Perfus_m(index_Width_Perfus),... Height_Perfus_m(index_Height_Perfus),... Tube_rsrv_inlet_m(index_Tube),... Q_perf_in(index_Q_perfus),... P_CPB_Pa(index_CPB),... Pore_diam_um(index_Pore),... Length_m, N, string_varying_variables);

end end end end end end end end display(' '); display('Data has been written to Excel file'); display('^^^^^^^^^^^^ E N D ^^^^^^^^^^^^'); display('==============================='); display(' ');display(' ');display(' '); clear all

102

function [] = ResistCalc_AUTO(Width_Blood_m_fun, Height_Blood_m_fun, Width_Perfus_m_fun, Height_Perfus_m_fun, Tube_rsrv_inlet_m_fun, Q_perf_in_fun, P_CPB_Pa_fun, Pore_diam_um_fun, Length_m_fun, N_fun, string_varying_variables_fun) % Declare Symbolic Variables syms P_rsrv Resist_rsrv Q_rsrv_in Q_pore P_perf Resist_perf Resist_pores syms Resist_tube dyn_visc_blood = 3.5e-3; %N-s/m^2 at 35C dyn_visc_perf = 1e-3; %N-s/m^2 dyn_visc_plasma = 1.6e-3; % Calculate Pore Resistance pore_boolean = 0; while (pore_boolean == 0) if Pore_diam_um_fun == .05 Pore_density = 6e8*(100)^2; Pore_thk = 6e-6; pore_boolean = 1; elseif Pore_diam_um_fun == .08 Pore_density = 6e8*(100)^2; Pore_thk = 6e-6; pore_boolean = 1; elseif Pore_diam_um_fun == .1 Pore_density = 3e8*(100)^2; % converts from per cm^2, to per m^2 Pore_thk = 6e-6; % [m] pore_boolean = 1; elseif Pore_diam_um_fun == .2 Pore_density = 3e8*(100)^2; Pore_thk = 10e-6; pore_boolean = 1; elseif Pore_diam_um_fun == .4 Pore_density = 1e8*(100)^2; % converts from per cm^2, to

per m^2 Pore_thk = 10e-6; % [m] pore_boolean = 1; elseif Pore_diam_um_fun == .6 Pore_density = 3e7*(100)^2; Pore_thk = 10e-6; pore_boolean = 1; elseif Pore_diam_um_fun == .8 Pore_density = 3e7*(100)^2; % converts from per cm^2, to

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per m^2 Pore_thk = 9e-6; % [m] pore_boolean = 1; else display(' '); display('Please enter correct pore size') display(' '); display(' '); end %if statement end % while statement Pore_diam_m = Pore_diam_um_fun*10^-6; % converts pore size diameter

from [um] to [m] Diff_Area_m2 = N_fun*Length_m_fun*min(Width_Perfus_m_fun,

Width_Blood_m_fun); % area is based on whichever width dimension is smallest

Num_Pores = Pore_density*Diff_Area_m2; Num_Pores; Fudge_rsrv_sumseries = 0; Fudge_perf_sumseries = 0; %%% additional fudge factor for Rectangular Duct Resistances %%% (simplified equation does not apply due to low aspect ratio

for ii=1:2:13 Fudge_rsrv_sumseries = Fudge_rsrv_sumseries +

(1/ii^5)*tanh(ii*pi*Width_Blood_m_fun/(2*Height_Blood_m_fun));

Fudge_perf_sumseries = Fudge_perf_sumseries + (1/ii^5)*tanh(ii*pi*Width_Perfus_m_fun/(2*Height_Perfus_m_fun));

end Fudge_rsrv = (1 - Height_Blood_m_fun/Width_Blood_m_fun *

(192/pi^5*Fudge_rsrv_sumseries))^-1; Fudge_perf = (1 - Height_Perfus_m_fun/Width_Perfus_m_fun *

(192/pi^5*Fudge_perf_sumseries))^-1; % Fudge_rsrv = 1; % Fudge_perf = 1;

%>>>>>>>>>>>>> SYMBOLIC EQUATIONS <<<<<<<<<<<<<<<<< eq1 = (P_CPB_Pa_fun-P_rsrv)/Resist_tube - P_rsrv/Resist_rsrv –

Q_pore; eq2 = Q_perf_in_fun + Q_pore - P_perf/Resist_perf;

eq3 = Q_pore - (P_rsrv/2-P_perf/2)/Resist_pores;

eq4 = Resist_rsrv - (12*dyn_visc_blood*Length_m_fun/

(Width_Blood_m_fun*Height_Blood_m_fun^3)/N_fun)*Fudge_rsrv;

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eq5 = Resist_perf – 12 * dyn_visc_perf*Length_m_fun/

(Width_Perfus_m_fun*Height_Perfus_m_fun^3)/N_fun* Fudge_perf;

eq6 = Resist_pores - 8*dyn_visc_plasma*Pore_thk/(pi*

(Pore_diam_m/2)^4) / Num_Pores; eq7 = Resist_tube - 8*dyn_visc_blood*Tube_rsrv_inlet_m_fun/

(pi*(0.28e-3/2)^4);

eq8 = Q_rsrv_in - (P_CPB_Pa_fun-P_rsrv)/Resist_tube; S = solve(eq1, eq2, eq3, eq4, eq5, eq6, eq7, eq8); %>>>>>>>>>>>>> SYMBOLIC EQUATIONS <<<<<<<<<<<<<<<<< format short eng P_rsrv = single(S.P_rsrv); % Pa P_perf = single(S.P_perf); % Pa Resist_rsrv = single(S.Resist_rsrv); Resist_perf = single(S.Resist_perf); Resist_pores = single(S.Resist_pores); Resist_tube = single(S.Resist_tube); Q_rsrv_in = single(S.Q_rsrv_in)/1.667e-11; % uL/min Q_perf_in_fun = single(Q_perf_in_fun)/1.667e-11; % uL/min Q_pore = single(S.Q_pore)/1.667e-11; % uL/min Q_rsrv_out = single(S.P_rsrv/S.Resist_rsrv)/1.667e-11; % uL/min Q_perf_out = single(S.P_perf/S.Resist_perf)/1.667e-11; % uL/min P_CPB_mmHg_fun = single(P_CPB_Pa_fun)/133.3; note = string_varying_variables_fun;

% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % S T O R I N G D A T A I N E X C E L % %

% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %

Header_title = {'0','Note','Reservoir Channel Width (um)','Reservoir Channel Height (um)',... 'Perfusion Channel Width (um)','Perfusion Channel Height (um)','Channel Length (mm)',... 'Number of Channels','Reservoir Tubing Length (in)','Pore Size (um)',... 'Perfusion Flow Rate (uL/min)','CPB Inline Pressure (mmHg)',...

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'Reservoir Pressure (Pa)','Perfusion Pressure (Pa)','Reservoir Channel Resistance',... 'Perfusion Channel Resistance','Pore Resistance','Reservoir Tubing Resistance',... 'Reservoir Flowrate-In (uL/min)',... 'Pore Flowrate (uL/min)','Reservoir Flowrate-Out (uL/min)',... 'Perfusion Flowrate-Out (uL/min)', 'Perf Flowrate Rec%'}; xlswrite('VolumeCalc_AUTO',Header_title,'Sheet1'); % % targetSheet = worksheets.Item('Sheet1'); % targetSheet.Activate; % % Check Excel sheet to make sure where data was last written, prevents % % writing over previous data [numrow, numcol] = size(xlsread('VolumeCalc_AUTO','Sheet1')); row = num2str(numrow + 1); col = 'A'; location = [col row]; write_excel = {0,note, Width_Blood_m_fun*1e6,

Height_Blood_m_fun*1e6, Width_Perfus_m_fun*1e6,... Height_Perfus_m_fun*1e6, Length_m_fun*1e3, N_fun,

Tube_rsrv_inlet_m_fun/.0254, Pore_diam_um_fun,... Q_perf_in_fun, P_CPB_mmHg_fun, P_rsrv, P_perf, Resist_rsrv, Resist_perf, Resist_pores, Resist_tube, Q_rsrv_in, Q_pore, Q_rsrv_out, Q_perf_out, Q_perf_out/Q_perf_in_fun*100};

xlswrite('VolumeCalc_AUTO',write_excel,'Sheet1',location); % display(' '); % display('Data has been written to Excel file'); % display('^^^^^^^^^^^^ E N D ^^^^^^^^^^^^'); % display('==============================='); % display(' ');display(' ');display(' '); % clear all; end % function

CONTINUOUS MICRODIALYSIS OF BLOOD PROTEINS DURING ...

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